Attal said in a post on X that the decision, which comes months before Paris hosts the Olympic Games, was taken "in light of the Islamic State's claiming responsibility for the (Moscow) attack and the threats weighing on our country".
France's terror alert system has three levels, and the highest level is activated in the wake of an attack in France or abroad or when a threat of one is considered to be imminent.
It allows for exceptional security measures such as stepped-up patrols by armed forces in public places like train stations, airports and religious sites.