Hollande "reiterated his wish for the negotiations on Britain's departure from the European Union to be undertaken as soon as possible", the president's office said yesterday in a statement after the two leaders spoke by phone.
Both also expressed their commitment to the further development of the amicable ties between their countries, it added.
One of May's first decisions will be when she plans to trigger Article 50 -- the formal procedure for withdrawal from the EU -- which would set a two-year deadline for completing exit negotiations.
May said last month that if she became prime minister she would not invoke Article 50 this year, despite pressure from EU leaders to do so swiftly.
Earlier yesterday, European Commission President Jean-Claude Juncker and European Parliament President Martin Schulz also urged May not to delay the Brexit divorce proceedings.
May's first meeting with key EU leaders could be at the G20 summit in China on September 4, but her first encounter with all of the other 27 EU leaders will be at the next European Council summit on October 20-21.