ASTX660 and Radiotherapy for Locally-Advanced Rectal Cancer

Inclusion Criteria: Locally advanced rectum cancer where primary resection without chemoradiotherapy is unlikely to achieve clear margins as defined by: * a distance between the tumor or its lymph node and the mesorectal fascia ≤ 2 mm on the pelvic MRI at diagnosis. * \*and/or N2 * No evidence of metastatic disease on CT-scan (chest and abdomen), including resectable metastases * Age : ≥ 18 years old at the time of informed consent * Successfully received at least 4 cycles and up to 6 cycles of mFOLFIRINOX (LCRT arm only) * Eastern Cooperative Oncology Group (ECOG) performance status (PS): 0 or 1 * Acceptable organ functions, as evidenced by the following laboratory data: * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤2.0×upper limit of normal (ULN) * Total serum bilirubin ≤1.5×ULN * Absolute neutrophil count (ANC): ≥2,000 cells/mm\^3 * Platelet count: ≥100,000 cells/mm\^3 * Hemoglobin: ≥ 9.0 g/dL * Serum creatinine levels ≤1.5×ULN, or calculated (by Cockcroft-Gault formula or other accepted formula) or measured creatinine clearance ≥50 mL/min * Amylase and lipase ≤1.5xULN * Adequate blood coagulation function as evidenced by an International Normalized Ratio (INR) ≤ 1.5. * Women of childbearing potential must have a negative serum β-HCG pregnancy test within 3 days prior to the administration of the first study treatment and/or urine pregnancy 12 hours prior to the administration of the first study treatment. * Female subjects of childbearing potential should be willing to use a highly effective method of contraception or be surgically sterile, or abstain from heterosexual activity for the course of the study through 6 months after the last dose of study medication. Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 6 months after the last dose of study therapy. * Also, it is recommended that women of childbearing potential partner use a highly effective method of contraception. * Patient should understand, sign, and date the written informed consent form prior to any protocol-specific procedures performed. Patient must be able and willing to comply with study visits and procedures as per protocol. * Patient must be affiliated to a social security system or beneficiary of the same. Exclusion Criteria: * Any contraindications to MRI (e.g. subjects with pacemakers, claustrophobia, excessive weight, etc). * Participation in another clinical study with an investigational product during the last 3 months. * No other anticancer therapy during study participation. (however, informed consent can be signed during mFOLFIRINOX for patients willing to enter the LCRT arm). * Hypersensitivity to tolinapant (ASTX660) or excipients of the drug product, or to any other component of the study treatment regimen, including: * 5-FU, capecitabine and known dihydropyrimidine dehydrogenase (DPD) deficiency, or * Oxaliplatin, or * Irinotecan and known Gilbert disease or genotype UGT1A1 (LCRT arm only) * Previous radiotherapy in the pelvic region * Preexisting condition that would deter radiotherapy, e.g. fistulas, severe ulcerative colitis (including subjects currently taking sulphasalazine), active Crohn's disease, prior adhesions * Preexisting condition that would deter chemotherapy, e.g. pneumonitis, pulmonary fibrosis, pernicious anemia or other anemias caused by vitamin B12 deficiency * Prior rectal surgery * Prior investigational treatment for rectal cancer * Poor medical risk because of systemic diseases (e.g., uncontrolled infections, uncontrolled diabetes) in addition to the qualifying disease under study * Life-threatening illness, significant organ system dysfunction, or other condition that, in the investigator's opinion, could compromise subject safety or the integrity of the study outcomes, or interfere with the absorption or metabolism of tolinapant (ASTX660) * A history of, or at risk for, cardiac disease, as evidenced by 1 or more of the following conditions: * Abnormal left ventricular ejection fraction (LVEF; \<50%) on echocardiogram (ECHO) or multiple-gated acquisition scan (MUGA) * Congestive cardiac failure of ≥ Grade 3 severity according to New York Heart Association (NYHA) functional classification defined as subjects with marked limitation of activity and who are comfortable only at rest * Unstable cardiac disease including unstable angina or hypertension as defined by the need for overnight hospital admission within the last 3 months (90 days) * History or presence of complete left bundle branch block, third-degree heart block, cardiac pacemaker, or clinically significant arrhythmia * Concurrent treatment with any medication that prolongs QT interval and may induce torsades de pointes and which cannot be discontinued at least 2 weeks before treatment with tolinapant (ASTX660) * Personal history of long QTc syndrome or ventricular arrhythmias including ventricular bigeminy * Screening 12-lead ECG with measurable QTc interval (according to either Fridericia's or Bazett's correction) of ≥470 msec) * Any other condition that, in the opinion of the investigator, could put the subject at increased cardiac risk * Refractory nausea and vomiting, chronic gastrointestinal diseases (eg, inflammatory bowel disease and/or bowel obstruction), or significant bowel resection that may impair adequate absorption and bioavailability of study drug. Major disturbance of bowel function (e.g. gross fecal incontinence or requiring \> 6 mg loperamide each day). * Known history of human immunodeficiency virus (HIV) infection; or seropositive results consistent with active hepatitis B virus (HBV) or active hepatitis C virus (HCV) infection. * Peripheral sensory neuropathy grade \>2 * Pregnancy or ongoing breastfeeding * Patient under guardianship or deprived of his liberty by a judicial or administrative decision or incapable of giving its consent. Yellow fever vaccine and live attenuated vaccines are contraindicated due to risk of severe vaccine-induced infection. NB : * The currently authorized COVID-19 vaccines are not live vaccines and therefore can be safely administered. * For patients registered in LCRT, all eligibility criteria will be fulfilled during mFOLFIRINOX (until 2 weeks after the end of mFOLFIRINOX). * For patients registered in SCRT, all eligibility criteria will be fulfilled before any treatment.