Environment and Fishing Commissioner Virginijus Sinkevicius raised the demand in a meeting with Britain's Environment Secretary George Eustice, said an EU spokesperson.
France had asked the commission to be "more active" in resolving the dispute.
"The commission must give a deadline to the U.K.," said French Fisheries Minister Annick Girardin.
France is demanding more fishing licenses from London and the Channel Island of Jersey as part of the post-Brexit agreement signed in late 2020.
European fishers can continue to work in British waters as long as they can prove that they fished there previously.
But the French and British are arguing over the nature and extent of the evidence required.
The spokesperson for the British government told the Express that the UK will not change its stance despite the deadline set by the EU.