Hollande was speaking after talks with British PM Theresa May in Paris on Thursday night, during which he warned the Tory leader that France would not allow Britain to remain in the free market unless it accepted freedom of movement.
Either "remain in the single market and assume the free movement that goes with it or to have another status," Hollande warned the UK.
The question of freedom of movement is crucial for the tens of thousands of British nationals living and working in France, many of whom fear that Brexit will make life more complicated, perhaps even impossible, in their adopted country.
While negotiations are yet to begin on any Brexit deal, Hollande tried to ease the fears of those expats both in the France and the UK, who have been left in limbo after the shock June referendum result.
“The UK will remain a full member of the EU throughout the negotiations process so nothing will change four our citizens. After the negotiations the rules will be set,” Hollande told a press conference.
“There's no doubt that the French who reside in the UK and the Britons who live in France will continue to work there and spend as much time as they like there,” the president added.
But many of those Britons living in France were hardly reassured by the statement.
In the Facebook support group Remain in France Together (RIFT) many pointed out the Hollande failed to mention a huge sector of the British population living in France.
“He's only talking about people working in France thus far- did not mention retired people,” said David Rosemount.
For many Brits in France the key issue will be whether they will continue to have access to health care post Brexit and their pensions.
“He says nothing,” said Dominic Rippon. “Even if we can stay to work, will we have healthcare subsidies cut? We'll have to wait a while for any detail, this is just politicking.”
Alan Court said: “Feel very concerned that the UK may abandon our healthcare and lock our pensions. Very worrying times that could go on for years.
Many were sceptical given that we are far from having anything set out in writing let alone in law.
Ruth Trevanion said: “This is just words, and there is no mention of those who don't work. I'll believe it when i see the signed agreement but it is a step in the right direction.”
As others pointed out there is also the fact that Hollande may not be around when Brexit negotiations begin, given that there is a presidential election in April next year and his popularity ratings are dismal.
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The same worries Brits have in France are mirrored by French nationals living in the UK, all of whom were barred from having a vote in the EU referendum.
Christophe Premat, the MP who represents French citizens living in the UK told The Local he has been inundated with queries from worried French expats.
“They all have questions regarding the consequences: what will happen to their child benefit or work benefits?” he said. “Students are also worried about university fees.”
“A lot of people here are talking about taking British nationality. That's a very personal decision, but if it's just for fiscal or administrative purposes I would say it's a shame, but if it's to participate in UK politics and they have been established here for a few years then it's a good choice," Premat said.
The lawmaker said he has also been approached by many French in the UK who are talking about returning home to France due to the uncertainty.
“Many are worried about the future. Some of those who have been established here and were thinking of returning home intend to shorten their stay in the UK,” he said.
The MP is confident bilateral relations will be sorted out between Britain and France that will guarantee the status of each country's citizens living abroad.
“Given that bilateral relations are already strong, not just in terms of defence and economy, that I believe we will be able to find agreements on things like tax reciprocity,” he said.
The MP also believes that Brexit should push Britain should copy the model of France and create an MP for the tens of thousands of British citizens living abroad.
“For those who live outside the UK and have no representation, then it could be a good compromise,” he said.
It may also force the Conservatives to fulfill their promise to scrap the law that bars expats who have lived abroad for more than 15 years from voting in national elections or referendums.