"We have received the first signals from the British authorities about accelerating the negotiations; a response to the French authorities' latest proposals is expected by Wednesday," Beaune tweeted.
"I have invited Lord Frost to Paris on Thursday for a more detailed discussion on the difficulties in implementing the agreements between the European Union and the United Kingdom," Beaune added.
Meanwhile, the measures that were announced by Paris against London will not come into effect before the meeting, according to the official.
The latest development emerged as the UK and France have been engaging in concerning rhetoric after Paris earlier warned that it may bar British fishing boats from some ports unless UK officials agreed to issue more licensing for its territorial waters.
France has been arguing that the UK granted 50% fewer licenses to French vessels than were outlined in post-Brexit negotiations.