The French president is also expected to say he rejects any "pre-negotiations" and has said the UK cannot access the EU free market without accepting the free movement of people.
Mr Hollande will host Ms May at a working dinner at the Élysée Palace, a day after she met with German Chancellor Angela Merkel in Berlin.
During their meeting on Wednesday, Ms Merkel made it clear Germany will not enter into discussions with the UK until it invokes Article 50 of the Lisbon Treaty and formally begins the two year process of leaving the EU.
“The people in the majority in the UK voted for leaving,” she said.
“We have not asked them to leave. I think it’s understandable that a new government will have to take a moment and seek to identify its interests," she added.
"So we will wait for the moment when the UK invokes this and applies for this and then we will put our guidelines on the table as to how we see the future relationship.”
Speaking in Dublin, Mr Hollande said: "The sooner the negotiations are open the better, and the shorter the better."
The Prime Minister has insisted she will not invoke Article 50 of the EU’s Treaty of Lisbon to start the talks until after the end of this year. She is sticking to the timescale she set out when she hoped to become prime minister in September, even though she succeeded David Cameron two months earlier than expected after her Tory leadership rivals all fell by the wayside.
Mr Hollande, speaking after talks with the Irish Prime Minister Enda Kenny, said: “Should the negotiations be shorter? The most important thing is that they should not drag on."
He added: "It's a decision that was taken by the British people...it is the British who will have to bare the consequences. Europe will try its best to give its best relationship with the UK. But there's a time the politicians have to accept this vote. They have to accept the consequences."
Ms May is adamant that she will not be rushed into opening the negotiations. Whitehall officials have warned her that the 27 other EU nations will be in the driving seat once they begin – partly because a two-year deadline for the process can be extended only if all 27 agree.
Responding to Mr Hollande’s remarks, Downing Street said Ms May had told him in a telephone call last week that “it was going to take some time to prepare for these negotiations.”
Her spokeswoman added: “France is one of our oldest and most important partners, where the depth of our relationship - particularly on security and defence - is very important for both of us. The PM's clear message will be the importance we attach to that relationship.”
Mr Kenny said Ireland's so-called “soft border” with Northern Ireland should remain after Brexit.
"We do not favour a hard border. Obviously we do not want to see a European border from Dundalk to Derry, that would not be acceptable.We'd be vigilant in terms of people moving through who might have tendencies to be involved in terrorist activities,” he said.
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