Inclusion Criteria:  A physician diagnosis of asthma for at least 12 months based on the Global Initiative for Asthma (GINA) 2018,2019, 2020 Guidelines. Participants with existing treatment with at least moderate to high doses of ICS therapy in combination with a LABA as second controller for at least 3 months with a stable dose ≥1 month prior to Visit 1. Participants with prebronchodilator FEV1 >40% of predicted normal at Visit 1/Screening. Prebronchodilator FEV1 ≥50% but ≤85% of predicted normal at Visit 2/Baseline. Participants with reversibility of at least 12% and 200 mL in FEV1 15 to 30 minutes after administration of 2 to 4 puffs (200-400 mcg) of albuterol/salbutamol or levalbuterol/levosalbutamol during screening or documented history of a reversibility test that meets this criteria within 12 months prior to Visit 1 or documented positive response to methacholine challenge (a decrease in FEV by 20% [PC20] of <8mg/mL) within 12 months prior to Visit 1/Screening is considered acceptable to meet this inclusion criterion. Participants must have experienced, within 2 years prior to Visit 1, any of the following asthma exacerbation events at least once: Treatment with a systemic steroid (oral or parenteral) for worsening asthma OR Hospitalization or emergency medical care visit for worsening asthma. Body mass index (BMI) ≥17.5 and ≤40 kg/m2 All Contraceptive use by men and women should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies.  Exclusion Criteria:  History of serious infections requiring intravenous therapy with the potential for recurrence or currently active moderate to severe infection at Screening (Grade 2 or higher) including active coronavirus disease 2019 (COVID-19). Chronic lung disease (for example, chronic obstructive pulmonary disease [COPD], or idiopathic pulmonary fibrosis [IPF]) which may impair lung function, or another diagnosed pulmonary or systemic disease associated with elevated peripheral eosinophil counts, for e.g. eosinophilic granulomatosis with polyangiitis. History of life-threatening asthma (i.e., severe exacerbation that requires intubation). Participants with any of the following events within the 4 weeks prior to their Screening Visit 1 or during the screening period: Treatment with 1 or more systemic (oral and/or parenteral) steroid bursts for worsening asthma OR Hospitalization or emergency medical care visit for worsening asthma Asthma Control Questionnaire 5-question version (ACQ-5) score <1.25 or >3.0 at V2/randomization. During the screening period an ACQ-5 of up to ≤4 is acceptable. Current smoker or cessation of smoking within the 6 months prior to Visit 1. Previous smoker with a smoking history >10 pack-years. Current or chronic history of liver disease. Known hepatic or biliary abnormalities. Symptomatic herpes zoster within 3 months prior to screening. Refractory nausea and vomiting, malabsorption, external biliary shunt, or significant bowel resection that would preclude adequate rilzabrutinib/placebo absorption. Conditions that may predispose the participant to excessive bleeding History of solid organ transplant. A history of malignancy of any type within 5 years before Day 1, other than surgically excised non-melanoma skin cancers or in situ cervical cancer. Is not up-to-date with recommended vaccinations per local guidelines. Anti-immunoglobulin E (IgE) therapy (e.g., omalizumab [Xolair®]) within 130 days prior to Visit 1 or any other biologic therapy (including anti-IL4/4R or IL-5/5R monoclonal antibodies [mAb]) or systemic immunosuppressant (e.g., methotrexate) to treat inflammatory disease or autoimmune disease (e.g., rheumatoid arthritis, inflammatory bowel disease, primary biliary cirrhosis, systemic lupus erythematosus, multiple sclerosis) and other diseases, within 2 months or 5 half-lives prior to Visit 1, whichever is longer. Use of inhalers other than ICSs, LABAs, and short-acting beta agonists (no long-acting muscarinic antagonists (LAMAs) or mucolytics) and leukotriene receptor antagonists (montelukast, zafirkulast) during the study period. Participants who have received bronchial thermoplasty within 2 years prior to Visit 1 or plan to begin therapy during the screening period or the randomized treatment period. Use of proton pump inhibitor drugs such as omeprazole and esomeprazole within 3 days of Day 1. Use of known strong-to-moderate inducers or inhibitors of CYP3A within 14 days or 5 half-lives (whichever is longer) of Study Day 1 and until the end of the active treatment period. Live vaccine except Bacille Calmette Guerinn-vaccination within 28 days prior to Day 1 or plans to receive one during the trial; Calmette Guerin-vaccination within 12 months prior to Screening. COVID-19 vaccine within 14 days prior to Study Day 1. Previous use of a Bruton tyrosine kinase (BTK) inhibitor. Has received any investigational drug (or is currently using an investigational device) within the 30 days before Day 1, or at least 5 times the respective elimination half-life time (whichever is longer). Electrocardiogram (ECG) findings of QT corrected for heart rate (QTc) >450 msec (males) or >470 msec (females), poorly controlled atrial fibrillation (i.e., symptomatic patients or a ventricular rate above 100 beats/min on ECG), or other clinically significant cardiovascular abnormalities. Positive COVID-19 molecular test at screening or at any time during the study except during the safety period.  The above information is not intended to contain all considerations relevant to a patient's potential participation in a clinical trial.