Efficacy of MEK (Trametinib) and BRAFV600E (Dabrafenib) Inhibitors With Radioactive Iodine (RAI) for the Treatment of Refractory Metastatic Differentiated Thyroid Cancer

Inclusion Criteria: * Patients with thyroid carcinoma of follicular origin (papillary, follicular or poorly differentiated and their respective variants) * Known positive RAS (NRAS or KRAS or HRAS) or BRAFV600E or K601E mutation (determined on a previous analysis and/or on a representative formalin-fixed paraffin embedded (FFPE) tumor samples sent for central testing or on a biopsy sample sent for central testing). * Radioiodine-refractory disease defined by at least one of the following item: 1. Distant metastasis without radioiodine uptake on a posttherapeutic radioactive scan 2. Distant metastasis disclosing RECIST progression within 12 months after a RAI treatment * Measurable disease with at least one lesion \>/= 1.0 cm in the longest diameter for a non-lymph node or \>/= 1.5 cm in the short axis for a lymph node, measured with spiral computed tomography (CT) without iv contrast injection or magnetic resonance imaging (MRI) according to RECIST 1.1 * Progressive disease according to RECIST 1.1 criteria within 18 months prior initiation of treatment * Absence of metastatic lesion \> 30mm * Previous cumulated activity of radioactive iodine ≤ 600 mCi (22.2GBq) * Patients may have received prior treatment with either 1 line of Tyrosine Kinase Inhibitor or 1 line of immunotherapy (excluding anti BRAF or anti MEK treatment such as sorafenib, dabrafenib, trametinib and selumitinib) but should be off treatment within 28 days prior to treatment start * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 * Blood pressure (BP) ≤ 140/90 mm Hg at screening with or without antihypertensive medications and no change in antihypertensive medications within 1 week prior to Cycle 1/Day 1 * Creatinine clearance ≥50 mL/min according to the Cockcroft and Gault formula * Adequate bone marrow function with : 1. Absolute neutrophil count (ANC) ≥1.5 x 109/L 2. Hemoglobin ≥9.0 g/dL 3. Platelet count ≥100 x 109/L 4. Normal blood coagulation function as evidenced by an International Normalized Ratio (INR) ≤ 1.5 * Adequate liver function with: 1. Bilirubin ≤1.5 × upper limit of normal (ULN) except for unconjugated hyperbilirubinemia or Gilbert's syndrome, 2. Alkaline phosphatase (ALP), alanine aminotransferase (ALT), and aspartate aminotransferase (AST) ≤3 × ULN (≤5 × ULN if subject has liver metastases). * Males or females age ≥ 18 years at the time of informed consent * Women of childbearing potential must have a negative urine or serum β-HCG pregnancy test within 7 days prior to the administration of the first study treatment. Sexually active women of childbearing potential must agree to use a highly effective method of contraception during the study and for at least 12 months after the last study treatment administration. Sexually active males patients must agree to use condom during the study and for at least 12 months after the last study treatment administration. Also, it is recommended their women of childbearing potential partner use a highly effective method of contraception. * In case of previous external beam radiation, all radiation therapy related toxicities must have resolved to \< Grade 2 severity per Common Terminology Criteria for Adverse Events (CTCAE v 4.0), except alopecia and infertility. * Voluntary agreement to provide written informed consent and the willingness and ability to comply with all aspects of the protocol * Patient affiliated to a social security regimen or beneficiary of the same Exclusion Criteria: * Undifferentiated or Medullary (MTC) carcinoma of the thyroid * Brain metastases (including asymptomatic brain metastases) * Major surgery within 4 weeks prior to the first dose of drug * Subjects having \> 1 + proteinuria on urine dipstick testing will undergo 24 h urine collection for quantitative assessment of proteinuria. Subjects with urine protein ≥ 1 g/24 h will be ineligible. * Need for locoregional treatment such as surgery, external beam radiation or thermoablation at inclusion * Prior RAI therapy \< 6 months prior initiation of treatment * External beam radiation \< 4 weeks prior initiation of treatment * Iodine contamination defined by a urine ioduria ≥ 50 μg/dl * Gastrointestinal malabsorption or any other condition that in the opinion of the investigator might affect the absorption of the drugs * History of congestive heart failure greater or equal to than New York Heart association (NYHA) Class II, unstable angina, myocardial infarction or stroke within 6 months of the first dose of drug, or cardiac arrhythmia associated with significant cardiovascular impairment and uncontrolled hypertension * Electrocardiogram (ECG) with QT interval (QTc) interval ≥480 msec * Active hemoptysis (bright red blood of at least 0.5 teaspoon) within 2 months prior to the first dose of drug and any other active bleeding, coagulopathy or pathologic condition that would confer a high risk of bleeding. * Active infection requiring systemic therapy * Active malignancy (except for DTC, or definitively treated melanoma insitu, basal or squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix or bladder) within the past 24 months * Any history of or concomitant medical condition that, in the opinion of the investigator, would compromise subject's ability to safely complete the protocol * Females who are pregnant or breastfeeding * Patients with an injection of radio-contrast agent within 8 weeks prior enrolment * Previous history of retinal vein occlusion * Previous history of central serious retinopathy * Known hypersensitivity to the study drugs or to any of the excipients