The UK and France will remain "tied by bonds of friendship" for decades after Brexit, Jeremy Hunt has said.
The foreign secretary lauded the cross-channel relationship as "one of competition, co-operation, similarity and difference" in a speech in Paris.
Officials said the visit was aimed at showing the friendship between the two nations was "bigger than Brexit".
But there are warnings intelligence-sharing may be damaged if a framework is not set up to mitigate the risks.
A report by an Anglo-French task force whose members include former Nato Secretary General Lord Robertson and ex-French Prime Minister Bernard Cazeneuve has said co-operation in cyber security and counter-terrorism could be imperilled if the UK leaves in March without an overarching agreement.
The Brexit process is at a critical phase amid reports Theresa May may seek the approval of her cabinet within days to sign up to an agreement on the terms of the UK's' withdrawal.
Mr Hunt is one of a group of leading ministers reported to be insisting on seeing legal advice in full on the conditions of any agreement on the Irish border and how a so-called backstop arrangement - of the UK staying in a customs union to avoid the need for a visible Northern Ireland border - would work.
After his speech Mr Hunt was asked about the legal advice. He said: "We have an excellent attorney general and he is giving very good legal advice on everything that we are considering signing up to, so we are going into this with our eyes open".
"That's very important because the Withdrawal Agreement is a legal document so we need to understand all the legal implications - and of course ultimately whatever the Cabinet decide to endorse will come before parliament and all these issues will be debated in full."
He was also asked if the UK and the EU were likely to agree a deal in the next three weeks, replying: "We are in the final phase and I think it is possible to be optimistic about the fact that we are essentially down to a couple of big issues... we are focusing all our efforts on those two issues but I think it's entirely possible to reach an agreement and everyone wants to do that."
'A big country'
Former Brexit Secretary David Davis told BBC Radio 4's Today programme it was the biggest decision the cabinet and Parliament will have to make, so they should be given the full legal advice.
Mr Davis said that he believed that if it was left to the EU to decide when the temporary backstop ended it would "never happen".
He predicted that the emerging Brexit deal would not be backed by MPs - although he told Today a defeat in the Commons would be likely to lead to the two sides hammering out what he called a better deal.
However he insisted that if there was no deal, the UK was a "big country" able to "look after ourselves" and had hundreds of plans prepared, although there would be some "hiccups over the first year".
France has taken an uncompromising line on Brexit, with its President Emmanuel Macron lashing out at the UK at a summit in Austria in September, saying its exit could not be allowed to undermine European unity.
But French industries also sense an opportunity to lure jobs from London, particularly in the financial services, after the UK leaves.
Uncertainty has surrounded bilateral Anglo-French immigration agreements after Brexit although the UK has made it clear it wants these to continue, along with the two countries' advanced defence co-operation.
In his speech, delivered in French, Mr Hunt hailed what he said had been nearly 200 years of cross-channel co-operation.
He paid tribute to Anglo-French solidarity, which he said was encapsulated by France's emphatic response to the poisonings of the Skripals in Salisbury earlier this year and last year's terror attacks in London.
"We will never forget the moment after the Manchester attack when President Macron walked from the Elysee Palace to the British Embassy to express France's solidarity," he said.
"And the crowd at the Stade de France sang the British national anthem - nor, when, after the Bataclan attack, the crowd at Wembley sang the Marseillaise."
Ahead of the centenary of the end of World War One on Sunday, Mr Hunt said the two countries' destinies were "yoked together" by the conflict "in which we fought and bled side by side for over four years".
The foreign secretary is also holding talks with his French counterpart Jean-Yves Le Drian on defence, national security and cyber-security.
The meeting comes amid calls for the two largest military powers in Europe to step up their co-operation by consolidating a series of bilateral agreements in place since 2010.
The BBC's security correspondent Frank Gardner said Whitehall officials were insisting intelligence sharing exists outside the framework of the EU and they expect it to survive the upheaval of Brexit.