PARIS—French President François Hollande delivered a sharp critique of the Obama administration in comments published Wednesday, calling Washington afraid to use its power to stop the bloodshed in Syria but too eager to wield its economic might to penalize European companies.

The comments reflect a divide between France and the U.S. over how to respond to Russia’s bombardment of Aleppo, combined with long-simmering anger at Washington’s power to target European companies, most recently Deutsche Bank AG with an expected multibillion-dollar...