Inclusion Criteria:
* Female 18 years of age or older
* Histologically confirmed recurrent unresectable or metastatic cervix carcinoma with squamous cell, adenocarcinoma or adenosquamous histology - - Patient may have received at least one prior chemotherapy regimen of platinum-based chemotherapy for recurrence or metastatic disease.
* Cisplatin given in combination with radiation for a localized disease does not count as a prior chemotherapy.
* Prior treatment for advanced/metastatic disease with bevacizumab is allowed.
* Prior treatments with immune checkpoint inhibitors are allowed. - ECOG performance status 0-2 - Measurable disease per RECIST 1.1
* The subject must have recovered to baseline or CTCAE v.5.0 (Common Terminology Criteria for Adverse Events, version 5.0) ≤ Grade 1 from clinical toxicities related to any prior treatments, i.e chemotherapy or pelvis radiation unless AE(s) are clinically non-significant (for example alopecia)
* Adequate organ and marrow function, defined as follows, based upon laboratory tests performed within 7 days before inclusion:
* Absolute neutrophil count (ANC) ≥ 1000/mm3 (≥ 1.0 GI/L)
* Platelets ≥ 100,000/mm3 (≥ 100 GI/L)
* Hemoglobin ≥ 10 g/dL (≥ 100 g/L) (red blood cell transfusion is allowed)
* Total bilirubin ≤ 1.5 fold the upper limit of normal (for subjects with Gilbert's disease, ≤ 3 mg/dL or ≤ 51.3 μmol/L) o Serum albumin ≥ 3.0 g/dL (≥ 30 g/L)
* Calculated creatinine clearance ≥ 30 mL/min by the CKD-EPI method.
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 3.0 x the upper limit of normal
* Urine protein/creatinine ratio (UPCR) ≤ 1g/g (≤ 113.17 mg/mmol creatinine) or 24-hour urine protein \< 1 g
* Left-ventricular ejection fraction ≥ 50%
* Subjects affiliated to an appropriate social security system
* Female subjects of childbearing potential must not be pregnant at screening and during treatment by Cabozantinib. Effective methods of contraception should be used throughout the course of treatment and for at least 4 months after the end of treatment. Sexually active fertile subjects and their partners must agree to use medically accepted barrier methods of contraception (e.g., male or female condom) during the study and 4 months after the last dose of study treatment, even if oral contraceptives are also used.
* Before patient registration, written informed consent must be given according to ICH/GCP, and national/local regulations.
Exclusion Criteria:
* Clinically significant gastrointestinal abnormalities that may increase the risk for gastrointestinal bleeding and/or fistula / perforation including, but not limited to: Active peptic ulcer disease, inflammatory bowel disease (e.g. ulcerative colitis, Crohn's disease), history of abdomino and/or pelvic fistula, gastrointestinal perforation, or intra-abdominal abscess, gastro-intestinal obstruction
* Patients with lesions on baseline pelvic MRI which may major the risk of abdominal and/or pelvic fistula/perforation
* Clinically significant gastrointestinal abnormalities that may affect absorption of investigational product including, but not limited to: malabsorption syndrome, major resection of the stomach or small bowel.
* Previously identified allergy or hypersensitivity to components of the study treatment formulations (Note: patients with rare hereditary problems of galactose intolerance, the Lapp lactase deficiency or glucose-galactose malabsorption should not take cabozantinib and are also excluded).
* History of any one or more of the following cardiovascular conditions within the past 6 months: Cardiac angioplasty or stenting, myocardial infarction, unstable angina, coronary artery bypass surgery, symptomatic peripheral vascular disease, class III or IV congestive heart failure, as defined by the New York Heart Association (NYHA), serious cardiac arrythmias.
* Corrected QT interval (QTc) calculated by the Fridericia formula \> 500 msec within 28 days before inclusion (see Annex for Fridericia formula). Note: if initial QTcF is found to be \> 500 msec, two additional ECGs separated by at least 3 minutes should be performed. If the average of these three consecutive results for QTcF is ≤ 500 msec, the subject meets eligibility in this regard.
* Uncontrolled hypertension defined as systolic blood pressure (SBP) of \> 150 mmHg or diastolic blood pressure (DBP) of \> 100 mmHg despite an optimal treatment.
* History of cerebrovascular accident including transient ischemic attack (TIA), symptomatic pulmonary embolism or untreated deep venous thrombosis (DVT) within the past 6 months. Note: Subjects with recent DVT or asymptomatic pulmonary embolism who have been treated with therapeutic anti-coagulating agents for at least 4 weeks are eligible.
* Major surgery or trauma within 28 days prior to first dose of investigational product and/or presence of any non-healing wound, fracture, or ulcer.
* Evidence of active bleeding or pathologic conditions that carry high risk of bleeding such as coagulopathy or tumor involving major vessels.
* At least 6 weeks must have elapsed between the last dose of pelvis palliative radiation and the first dose of cabozantinib or 2 weeks for other localization of palliative radiation
* Presence of brain metastases or epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 3 months before inclusion. Eligible subjects must be neurologically asymptomatic and without corticosteroid treatment at the time of inclusion.
* Concomitant use of known strong CYP3A4 inhibitors or inducers.
* Patients with second primary cancer, except adequately treated non-melanoma skin cancer, or other solid tumors curatively treated with no evidence of disease for ≥ 3 years
* Any psychological, familial, sociological or geographical condition potentially hampering compliance with the study protocol and follow-up schedule; those conditions should be discussed with the patient before registration in the trial
* Concurrent participation in any therapeutic clinical trial
* Patient deprived of liberty or placed under the authority of a tutor
