The Prime Minister defended her decision to withdraw the UK from the single market and try to negotiate a trade deal with the EU, saying this did not amount to trying to unfairly keep hold of the best aspects of membership.
Her comments came as she prepares to host Bernard Cazeneuve, the French Prime Minister, for talks at Downing Street on Friday.
Ms May has previously said she wants the UK to maintain the “greatest possible access” to the EU trading bloc – triggering warnings from other European leaders that she would not be able to “cherry pick” during Brexit negotiations.
The Prime Minster has denied this is her aim. Writing in 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.
"We do not, to borrow the phrase, seek to cherry-pick which bits of membership we desire."
In the article, Ms May also argued it was in France’s interest to help Britain secure a trade deal with the EU, because French companies benefit from €50 billion of annual trade between the two countries.
What experts have said about Brexit
What experts have said about Brexit
1/11 Chancellor of the Exchequer Philip Hammond
The Chancellor claims London can still be a world financial hub despite Brexit “One of Britain’s great strengths is the ability to offer and aggregate all of the services the global financial services industry needs” “This has not changed as a result of the EU referendum and I will do everything I can to ensure the City of London retains its position as the world’s leading international financial centre.”
2/11 Yanis Varoufakis
Greece's former finance minister compared the UK relations with the EU bloc with a well-known song by the Eagles: “You can check out any time you like, as the Hotel California song says, but you can't really leave. The proof is Theresa May has not even dared to trigger Article 50. It's like Harrison Ford going into Indiana Jones' castle and the path behind him fragmenting. You can get in, but getting out is not at all clear”
3/11 Michael O’Leary
Ryanair boss says UK will be ‘screwed’ by EU in Brexit trade deals: “I have no faith in the politicians in London going on about how ‘the world will want to trade with us’. The world will want to screw you – that's what happens in trade talks,” he said. “They have no interest in giving the UK a deal on trade”
4/11 Tim Martin
JD Wetherspoon's chairman has said claims that the UK would see serious economic consequences from a Brexit vote were "lurid" and wrong: “We were told it would be Armageddon from the OECD, from the IMF, David Cameron, the chancellor and President Obama who were predicting locusts in the fields and tidal waves in the North Sea"
5/11 Mark Carney
Governor of Bank of England is 'serene' about Bank of England's Brexit stance: “I am absolutely serene about the … judgments made both by the MPC and the FPC”
6/11 Christine Lagarde
IMF chief urges quick Brexit to reduce economic uncertainty: “We want to see clarity sooner rather than later because we think that a lack of clarity feeds uncertainty, which itself undermines investment appetites and decision making”
7/11 Inga Beale
Lloyd’s chief executive says Brexit is a major issue: "Clearly the UK's referendum on its EU membership is a major issue for us to deal with and we are now focusing our attention on having in place the plans that will ensure Lloyd's continues trading across Europe”
8/11 Colm Kelleher
President of US bank Morgan Stanley says City of London ‘will suffer’ as result of the EU referendum: “I do believe, and I said prior to the referendum, that the City of London will suffer as result of Brexit. The issue is how much”
9/11 Richard Branson
Virgin founder believes we've lost a THIRD of our value because of Brexit and cancelled a deal worth 3,000 jobs: We're not any worse than anybody else, but I suspect we've lost a third of our value which is dreadful for people in the workplace.' He continued: "We were about to do a very big deal, we cancelled that deal, that would have involved 3,000 jobs, and that’s happening all over the country"
10/11 Barack Obama
US President believes Britain was wrong to vote to leave the EU: "It is absolutely true that I believed pre-Brexit vote and continue to believe post-Brexit vote that the world benefited enormously from the United Kingdom's participation in the EU. We are fully supportive of a process that is as little disruptive as possible so that people around the world can continue to benefit from economic growth"
11/11 Kristin Forbes
American economist and an external member of the Monetary Policy Committee of the Bank of England argues that the economy had been “less stormy than many expected” following the shock referendum result: “For now…the economy is experiencing some chop, but no tsunami. The adverse winds could quickly pick up – and merit a stronger policy response. But recently they have shifted to a more favourable direction”
"UK companies are responsible for an estimated 230,000 jobs in France, and French companies for about 370,000 jobs in the UK," she wrote.
The Prime Minister also stressed the UK will remain an "open and tolerant" country and that French people will "always be welcome in Britain".
She reiterated her aim of guaranteeing the rights of EU nationals already in the UK, including more than 300,000 French people, and said she hopes France will do the same for Britons living there.
"I will make securing this reciprocal agreement a priority as soon as the negotiations begin, because this is in everyone's interests," she said.
Ms May’s discussions with Mr Cazeneuve are likely to focus on Brexit and Russia. The Prime Minister warned of Moscow’s “aggressive and destabilising” actions in Ukraine, which she said have resulted in a “drastic deterioration” in the country.
The fight against terrorism is also likely be on the agenda after two years in which France has suffered several deadly attacks.
Ms May said the UK would “continue to stand shoulder to shoulder with France” and added: "In this period of change for my nation, Britain may be leaving the European Union as an organisation, but we will be stronger than ever as a dependable partner for our friends in France and across Europe, working to enhance the security and prosperity of all our citizens.
"As I said in my first speech as Prime Minister in the British Parliament, we share a firm belief in the values of liberte, egalite and fraternite. And together with France, a global Britain will always defend them."