On her first foreign trip since taking office in the wake of Britain's seismic June referendum, May told German Chancellor Angela Merkel on Wednesday that her government would not ask to leave the EU before the end of 2016 in order to plan a "sensible and orderly departure".
But there may be trouble ahead with France urging the UK to get on with the arduous and fraught task of divorcing itself from the EU.
Ahead of the meeting in Paris, Hollande flew to Ireland -- the EU country which will be most affected by Britain's decision to leave the 28-nation bloc.
In a joint statement Hollande and Ireland's Prime Minister Enda Kenny stressed the need for Britain to begin the Brexit process "as soon as possible" which will trigger "orderly negotiations".
Worried about growing euroscepticism at home, France has urged Britain not to draw out its negotiations to leave the European Union although it accepts that formal talks may not begin for several months.
"François Hollande has made it very clear, the British voted for it so we have to do it," Christophe Premat the MP who represents French nationals in the UK told The Local.
Premat says the French know little of Theresa May and the new PM is unlikely to get an easy ride during negotiations in Paris.
"Of course Britain will come to an agreement with the EU, but the French government does not want the UK to have all the benefits of being in the EU, without actually being a part of it," said Premat.
"It's important to complete Brexit as soon as possible, partly because it's important to respect the vote," said adding that the strong bilateral relations between Britain and France will stand the two countries in good stead when it comes to negotiations.
Diplomats close to Hollande also suggested the emphasis is firmly on the UK to deal with the fall out of the June referendum and will not get everything it asks for from Paris.
"The pressure is on Britain. It has put itself in this situation," a French diplomatic source told AFP.
The diplomat said Britain could not get a custom-made agreement on its future relations with the EU.
"That is not possible. It has to choose between existing options."
Speaking after his meeting with Kenny in Dublin Hollande said more specifically that: "Access to the single market cannot be guaranteed unless free movement of workers is respected."
Hollande has a presidential election looming next year and faces the far-right National Front, which wants France to leave the EU too.
Britain on Wednesday took the first step towards Brexit by announcing it was relinquishing its six-month EU presidency which had been due to start in July 2017 and will be taken up by Estonia instead.
But during her visit to Berlin, May said she would not initiate the formal procedure for Brexit "before the end of this year" at the earliest.
Merkel, who is expected to play a pivotal role in the Brexit talks along with France, said it was in the interests of all that Britain had a "well-defined position" before beginning the negotiations.
"No one wants things to be up in the air -- neither Britain nor the member states of the EU," Merkel said.