BRUSSELS—The European Union is preparing to reject France’s 2015 budget, according to European officials, setting up a clash that would be the biggest test yet of new powers for Brussels that were designed to prevent a repeat of the eurozone’s sovereign-debt crisis.

French Finance Minister Michel Sapin said last month that his country would run a budget deficit of 4.3% of gross domestic product next year—far from the 3% deficit it had previously pledged. Stripping out the effects of the weak economy, the government’s planned...