France is talking tougher about the proposed trade and investment pact between the U.S. and European Union, threatening to call the talks to a close if there isn’t more progress soon.

At a briefing in Brussels Tuesday, Matthias Fekl, secretary for international trade, reinforced a message of French frustration with aspects of the negotiations with Washington. His complaints about the negotiations over the so-called Trans-Atlantic Trade and Investment Partnership covered three main areas.

The...