President Trump lashed out at his French counterpart over military spending and trade on Tuesday, two days after returning from a trip to Paris that exposed the underlying tensions between the leaders.

In a series of tweets, Mr. Trump criticized French President Emmanuel Macron over his struggle to overhaul France’s economy, castigated Mr. Macron’s suggestion that Europe needs to be more self-sufficient in its own defense and called for France to contribute more to the North Atlantic Treaty Organization.

“Emmanuel...