EU leaders are pressuring Theresa May to trigger Article 50 right after Christmas
May intends to trigger Article 50 - Britain's formal notice that it intends to leave the EU and thereby starts the two-year negotiation period - in March next year, but that is only a month before the first round of French presidential elections.
Hollande will press May at an EU summit today to bring that date back nearer to Christmas, or even sooner.
That is because Hollande expects to re-run for president, despite being the most unpopular leader in French history.
And it will be difficult for Hollande to make any binding negotiations at an EU level if he is in the middle of an uncertain bid for re-election - he will be worried about making any commitments that would damage his chances.
The problem with May's intended timing is that once she sends the formal letter triggering Article 50, it will take weeks or months even to draw up a negotiating timetable. If she does that in March, negotiations will begin in the middle of the French presidential election, which begins on April 23.
Germany would also welcome the UK triggering formal negotiations sooner than March, given the huge uncertainty surrounding the current situation. A German official told the Financial Times that the country "an early start to negotiations" would be welcome.
German chancellor Angela Merkel will be facing her own elections in September, making May's potential timing of Article 50 difficult for her too.
In any case, negotiating Brexit will be very difficult for the UK. Countries, including France, wish to take a hard line with Britain, and give it as few concessions as possible in order to deter other countries from leaving the EU.
May is holding off triggering the process because she wants assurances that the country will get a favourable deal from Europe - May believes that could include being allowed to curb immigration while keeping a very favourable trade deal with the union.
But Hollande said last month that "there must be a threat, there must be a risk, there must be a price" when it comes to Britain leaving.