Theresa May stressed the importance of an early deal on EU citizens' rights after Brexit during talks with French prime minister Bernard Cazeneuve at Number 10.
The Prime Minister said she was "delighted" to welcome Mr Cazeneuve to Downing Street and pointed out they "worked so well together" when she was home secretary and he was France's interior minister.
The PM went on: "It's an interesting time, obviously for the UK, as we prepare to trigger Article 50 for leaving the European Union.
"But there are many issues on which the UK and France have been working very well and our bilateral relationship is very strong and I look forward to being able to develop that across a number of areas, including of course, our defence and security."
Following the talks a Downing Street spokeswoman said: "They talked about a range of bilateral issues and also discussed foreign policy and Brexit.
"The Prime Minister was clear that while the UK is leaving the EU, we are not leaving Europe, and they talked about the importance of coming to an early agreement on the rights of EU citizens in the UK and UK citizens in the EU.
"They agreed on the need to maintain our close cooperation on security and defence, including through Nato.
"They discussed how we can work together to address the shared global challenges we face, including migration, the situation in Syria and in Ukraine, and the threat of terrorism."
Ahead of the meeting Mrs May sought to reassure France the UK would not seek to "cherry-pick" which parts of European Union membership it wants to keep.
She said her aim to leave the single market, but strike a free trade deal with the EU, including the "greatest possible access" to the trade bloc, does not amount to selectively choosing the best aspects of membership.
After Mrs May set out her Brexit strategy last month, several leading EU figures warned the UK it will not be able to "cherry-pick" when it comes to negotiating a new relationship with Brussels.
But in an article for French newspaper Le Figaro, she said: "As we leave the EU, we will seek the greatest possible access to the European single market through a new, comprehensive, bold, ambitious free trade agreement.
"This cannot, however, mean retaining membership of the single market.
"(French) President (Francois) Hollande and other European leaders have been very clear that this would mean accepting the four freedoms of goods, capital, services and people and I respect their position.
"Britain understands that EU leaders want to continue with the process of integration.
"We do not, to borrow the phrase, seek to cherry-pick which bits of membership we desire."
Mrs May also highlighted French interest in a good Brexit deal, pointing out that the UK is France's fifth-largest export market with bilateral trade worth more than 50 billion euro last year.
"UK companies are responsible for an estimated 230,000 jobs in France, and French companies for about 370,000 jobs in the UK," she added.
Mrs May stressed the UK will remain an "open and tolerant" country and French people will "always be welcome in Britain".