"The sooner these negotiations begin the better, and the shorter they are the better," Hollande said after meeting Irish Prime Minister Enda Kenny in Dublin, calling for negotiations "as soon as possible".
"Things should not drag on," Hollande said, hours before he is due to meet British Prime Minister Theresa May in Paris for the first time.
He said he expected May to give her "reasons" on why she was planning to delay until next year invoking Article 50 of the EU's Lisbon Treaty -- the formal procedure for withdrawal from the European Union.
On her first foreign trip since taking office in the wake of Britain's seismic June referendum, May told Merkel that her government would not ask to leave the EU before the end of 2016 in order to plan a "sensible and orderly departure".
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.
He has a presidential election looming next year and faces a challenge from the far-right National Front, which wants France to leave the EU too.
The Brexit talks are expected to hinge on Britain's desire to restrict immigration of EU citizens but still retain vital access to the EU's single market.
Hollande appeared to rule out the possibility.
"Access to the single market cannot be guaranteed unless free movement of workers is respected," he said.
Hollande and Kenny also said in a joint statement that there should be "a balance of rights and obligations, including in respect of the four freedoms", referring to the free movement of goods, services, capital and people in the EU.
Brexit campaigners argued that the hundreds of thousands of EU immigrants arriving in Britain every year have been pushing down wages for low-paid Britons and overburdened public services.
Ireland's concerns revolve mainly around the future of its lucrative exports to Britain and its border with British-ruled Northern Ireland, which would be the EU's only land border with Britain once it has left.
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