Mr Hollande was speaking at a press conference with David Cameron at the conclusion of a one-day Anglo-French summit in the city of Amiens.
The summit was overshadowed by comments from French finance minister Emmanuel Macron, who suggested that migrant camps could be moved from Calais to the UK if Britain votes to leave the EU. Mr Hollande did not repeat his warning, but left no doubt that he wants a Remain vote in the referendum.
“I hope the UK remains in Europe,” said Mr Hollande. “It is in the interest of the UK, it is in the interest of Europe, but the people are always sovereign.” He then warned of “consequences” if the UK voted to leave: “I don’t want to scare you. I just want to say the truth.
“There will be consequences if the UK is to leave the EU, there will be consequences in many areas, in the single market, in the financial trade, in development, in the economic development between our two countries. It doesn’t mean that everything will be destroyed, I don’t want to give you catastrophic scenarios, but there will be consequences.”
Mr Hollande said the change would not put the relationship between the UK and France in question, but said: “There will be consequences, especially in the way we handle the situation in terms of immigration. There is no solution where there is no consequences.
“There are consequences if the In wins or if Out wins. There will be consequences both ways. Every time the people speaks out in a referendum, there are consequences.”
Mr Cameron said: “When you have ministers in other governments warning about potential consequences that might happen that would be injurious to the UK, I would say listen to those things.”
The Prime Minister announced £17 million of funding for enhanced security in Calais, as well as moves to relocate migrants from the port to facilities elsewhere in France. “I applaud the action that the French government is taking to deal with the situation with the camps in Calais and to say to people that they should be seeking asylum in France, and if they are not asylum seekers they should be returned to the countries from which they came,” he said.
“That, I think, is absolutely the right approach and the president has my 100 per cent backing in the work he is doing to deliver that. And as the money that we announced today shows, we are absolutely working in a joint endeavour.”
The Amiens summit also saw an agreement to jointly invest £1.5 billion to develop the next generation of unmanned combat air systems which Mr Cameron said will be “the most advanced of its kind in Europe, securing engineering jobs and expertise” in the UK and France.