• 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% 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 criterion within 5 years prior to Visit 1 or documented positive response to methacholine challenge (a decrease in FEV by 20% [PC20] of <8mg/mL) within 5 years 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.
• Participants must have completed COVID-19 vaccination per current regional health authority recommendations prior to screening.

• History of serious infections requiring intravenous therapy with the potential for recurrence (as judged by Site Investigator), with less than 4 weeks interval between resolution of serious infection and first dose of study drug, or currently active moderate-to-severe infection at Screening (Grade 2 or higher).
• 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, e.g. moderate or severe hepatic impairment, such as Child Pugh B or C
• 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 systemic 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.
• Active COVID-19 infection as documented by a positive COVID-19 molecular test.

        The above information is not intended to contain all considerations relevant to a patient's
        potential participation in a clinical trial.