Travelers from 34 new countries including France are exempt from tourist visa for stays of up to 30 days in Mongolia. Your Visa will be given to you upon arrival (stamp in your passport) and can be extended for an additional 30 days at the immigration office in Ulaanbaatar.
Before your departure, always check that the legislation has not changed with the government's Travel Advice website.
Official Mongolian Visa website: Evisa.mn