A French presidential adviser said on Friday that Paris refuses to put up with repeated extensions of the Brexit deadline.
The adviser underscored the necessity of finding a solution by 31 October.
The official raised hopes that the European Parliament election would prompt the UK political parties to reach a deal on the country's withdrawal from the European Union.
The French president, Emmanuel Macron, has assumed a hardline stance against a prolonged Brexit extension for the UK.
Britain was due to withdraw from the bloc by the end of March, but the EU granted it an extension until 31 October after PM May's Brexit deal was voted down by parliament on three separate occasions.
Theresa May's de-facto deputy David Lidington confirmed earlier this week that the UK would hold European elections set to take place 23 to 26 May 2019.