British Prime Minister Theresa May and French President François Hollande papered over their differences over how quickly the U.K. should exit the European Union in a bid to smooth choppy relations since Britons voted to leave the bloc.

The French leader has taken a firm stance since the June referendum, calling for a speedy U.K. exit and saying London risks losing its prominence as a European financial center. On Wednesday, Ms. May met German Chancellor Angela Merkel, who was more conciliatory, saying she understood that...