Worldwide observational studies indicate a significant prothrombogenic effect associated with SARS-CoV-2 infection with a high incidence of venous thromboembolism (VTE), notably life-threatening pulmonary embolism. According to recommendations for acute medical illnesses, all COVID-19 hospitalized patients should be given VTE prophylaxis such as a low molecular weight heparin (LMWH). A standard prophylactic dose (eg. Enoxaparin 4000IU once daily) could be insufficient in obese patients and VTE has been reported in patients treated with a standard prophylactic dose. In COVID-19 patients, guidelines from several international societies confirm the existence of an hypercoagulability and the importance of thromboprophylaxis but the "optimal dose is unknown" and comparative studies are needed. In view of these elements, carrying out a trial comparing various therapeutic strategies for the prevention of VTE in hospitalized patients with COVID-19 constitutes a health emergency. Thus, we hypothesize that an increased prophylactic dose of weight-adjusted LMWH would be greater than a lower prophylactic dose of LMWH to reduce the risk of life-threatening VTE in hospitalized patients. The benefit-risk balance of this increase dose will be carefully evaluated because of bleeding complications favored by possible renal / hepatic dysfunctions, drug interactions or invasive procedures in COVID-19 patients. This multicenter randomized (1:1) open-label controlled trial will randomize hospitalized adults with COVID-19 infection to weight-adjusted prophylactic dose vs. lower prophylactic dose of LMWH.