Inclusion Criteria:

        I1. Male or female patients aged of at least :

          -  Adult-Young Adult cohort: 12 years on day of signing informed consent.

          -  Pediatric Cohort: 6 months and maximum 11 years on day of signing informed consent.

        I2. Histologically-confirmed diagnosis of soft tissue sarcomas, confirmed by a pathologist
        from RRePS Network, among the 4 cohorts:

          -  Rhabdomyosarcomas (RMS).

          -  Malign Peripheral Nerve Sheath Tumors (MPNST).

          -  Complex genomics sarcomas including Undifferentiated Pleomorphic Sarcomas (UPS),
             leiomyosarcomas (LMS), Pleomorphic liposarcomas, angiosarcoma, myxofibrosarcomas.

          -  Single genomic sarcoma including Well and de-differentiated liposarcoma, myxoid
             liposarcoma, synovialsarcoma, alveolar soft part sarcoma, epithelioid sarcomas, and
             malignant rhabdoïd tumors.

        I3. Availability of a representative formalin-fixed paraffin-embedded (FFPE) primary and/or
        metastatic tumor tissue with an associated pathology report for molecular prescreening i.e.
        either an archival block or a dedicated freshly collected de novo tumor biopsy.

        I4. Documented MAPK pathway status and known Tumor Mutational Burden (TMB) before C1D1.

        I5. Previous treatment with anthracycline-based chemotherapy (in the neoadjuvant, adjuvant
        or metastatic setting). Note: this criteria not mandatory for rhabdomyosarcoma.

        I6. Previous treatment by at least one line of chemotherapy in the advanced/metastatic
        setting before C1D1.

        I7. Documented radiological disease progression as per RECIST V1.1 before C1D1.

        I8. At least one measurable lesion according to RECIST v1.1 before C1D1.

        I9. Mandatory for adult patients only - Presence of at least one tumor lesion visible by
        medical imaging and accessible to repeatable percutaneous sampling that permits core needle
        biopsy without unacceptable risk of a significant procedural complications, and suitable
        for retrieval of 4 cores using a 16-gauge diameter needle or larger.

        I10. Performance status:

          -  Lansky Play score for pediatric patients <12 years of age ≥ 70%;

          -  Karnofsky performance status for pediatric patients ≥12 years of age ≥ 70%;

          -  PS ECOG for adult patients: 0 or 1.

        I11. Life expectancy of at least 16 weeks.

        I12. Demonstrate adequate organ function based on screening laboratory tests performed
        within 7 days prior C1D1: Absolute neutrophil count ≥1.5 10 exp. 9/L; Platelets ≥100 10
        exp. 9/L; Hemoglobin ≥9 g/dL; Serum creatinine OR Creatinine clearance according to CKD-EPI
        for adult and C-KID formula for pediatric patients ≤1.5 X ULN OR ≥ 30 mL/min/1.73m2 for
        patient with creatinine levels > 1.5 ULN; Serum total bilirubin ≤ 1.5 X ULN OR Direct
        bilirubin ≤ ULN for patients with total bilirubin levels > 1.5 ULN; ASAT and ALAT and ALP ≤
        3 X ULN; INR and Activated Partial Thromboplastin Time (aPTT)≤1.5 X ULN.

        I13. Resolution (i.e. ≤ Grade 1 with the exception of alopecia all grades and Grade 2 for
        neuropathy, lab values presented in criteria I12.) of any toxicities related to previous
        anti-cancer treatment.

        I14. Women patient of child-bearing potential must have a negative serum pregnancy test
        before C1D1 and must agree to use effective forms of contraception from the time of the
        negative pregnancy test up to 6 months after the last dose of study drugs.

        I15. Sexually active and fertile men must agree to use contraceptive measures up to 5
        months after the last study drugs.

        I16. Written informed consent from patient, parents if applicable/legal representative,
        before any study-specific screening procedures, and willingness to comply to study visits
        and procedures.

        I17. Patients must be covered by a medical insurance.

        Exclusion Criteria:

        NI1. Soft tissue sarcoma disease considered curable with surgery or radiotherapy.

        NI2. Prior treatment with cobimetinib or other MEK inhibitors. NI3. Prior treatment with
        immune checkpoint blockade therapies, including anti-CTLA-4, anti-PD-1, or anti-PD-L1
        therapeutic antibodies.

        NI4. Patients with history of severe allergic or other hypersensitivity reactions to:

          -  Chimeric or humanized antibodies or fusion proteins,

          -  Biopharmaceuticals produced in Chinese hamster ovary cells, or

          -  Any component of the atezolizumab formulation.

          -  Any component of Cobimetinib formulation.

        NI5. History of malabsorption syndrome or other condition that would interfere with the
        absorption of oral medications.

        NI6. Symptomatic, untreated, or actively progressing central nervous system (CNS)
        metastases.

        Note: Asymptomatic patients with treated CNS lesions are eligible, provided that all of the
        following criteria are met:

          -  Measurable disease, per RECIST v1.1, must be present outside the CNS.

          -  No history of intracranial hemorrhage or spinal cord hemorrhage.

          -  Metastases are limited to the cerebellum or the supratentorial region (i.e., no
             metastases to the midbrain, pons, medulla, or spinal cord).

          -  No stereotactic radiotherapy within 7 days prior to initiation of study treatments,
             whole-brain radiotherapy within 14 days prior to initiation of study treatment,
             neurosurgical resection within 28 days prior to initiation of study treatments.

          -  No evidence of interim progression between completion of CNS-directed therapy and
             initiation of study treatments.

          -  No ongoing requirement for corticosteroids as therapy for CNS disease. Anticonvulsant
             therapy at a stable dose is permitted.

        NI7. History of or evidence of retinal pathology on ophthalmologic examination that is
        considered a risk factor for neurosensory retinal detachment, central serous
        chorioretinopathy, retinal vein occlusion (RVO), or neovascular macular degeneration.

        NI8. Left ventricular ejection fraction (LVEF) < institutional lower limit of normal
        (according to age) or < 50%.

        NI9. History of congenital long QT syndrome or corrected QT interval (QTc) > 450 ms.

        NI10. Patients using, or requirement to use while on the study, or not respecting the
        minimal wash-out period of medications listed below:

        Any approved anti-cancer systemic treatment including chemotherapy, hormonotherapy,
        biological therapy, or immunotherapy: 2 weeks; any investigational agents: 4 weeks;
        Radiotherapy: 3 weeks; major surgical procedure, open biopsy, or significant traumatic
        injury: 4 weeks; abdominal surgery, abdominal interventions or significant abdominal
        traumatic injury : 60 days; live vaccines : 4 weeks; systemic immunostimulatory agents,
        including but not limited to IFN-α, IFN-γ, or IL-2 : 4 weeks; immunosuppressive medications
        with the exceptions of intranasal, inhaled, or topical corticosteroids or systemic
        corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or
        an equivalent corticosteroid: 2 weeks; P-gp inhibitors : None; Strong or moderate
        inhibitors of CYP3A4 : None; Strong CYP3A4 inducers: None; oral or IV antibiotics : 2
        weeks.

        NI11. Patients with a malignancy other than STS within 5 years prior to C1D1 with the
        exception of those with a negligible risk of metastasis or death and treated with expected
        curative outcome

        NI12. History of autoimmune disease including but not limited to myasthenia gravis,
        myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis,
        inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome,
        Wegener's granulomatosis, Sjögren's syndrome, Guillain-Barre syndrome, multiple sclerosis,
        vasculitis, or glomerulonephritis with the following exceptions:

          -  patients with a history of autoimmune-related hypothyroidism who are on stable thyroid
             replacement hormone therapy,

          -  patients with controlled Type 1 diabetes mellitus,

          -  patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with
             dermatologic manifestations only (e.g., patients with psoriatic arthritis would be
             excluded) are eligible provided that they meet the following conditions:

          -  rash must cover less than 10% of body surface area (BSA).

          -  disease is well controlled at baseline and only requiring low potency topical
             steroids.

          -  no acute exacerbations of underlying condition within the previous 12 months requiring
             PUVA [psoralen plus ultraviolet A radiation], methotrexate, retinoids, biologic
             agents, oral calcineurin inhibitors, high potency or oral steroids.

        NI13. Patients with HIV, active B or C hepatitis infection, or any other active infection.

        Active hepatitis C i.e. Patients positive for hepatitis C virus (HCV) antibody are eligible
        only if PCR is negative for HCV RNA at screening.

        NI14. Patients with active tuberculosis. NI15. Prior allogeneic bone marrow transplantation
        or solid organ transplant for another malignancy in the past.

        NI16. History of idiopathic pulmonary fibrosis (including pneumonitis), drug-induced
        pneumonitis, organizing pneumonia (i.e. bronchiolitis obliterans, cryptogenic organizing
        pneumonia), or evidence of active pneumonitis on screening chest CT scan.

        NI17. Patients with a high-risk of hemorrhage or history of coagulopathy. NI18. Pregnant or
        breastfeeding women.