The Prime Minister 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.
Her comments come ahead of Downing Street talks on Friday with French prime minister Bernard Cazeneuve.
After Mrs May set out her Brexit strategy last month, several leading EU figures again 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 euros 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 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.
Mrs May and Mr Cazeneuve are also set to agree to maintain pressure on Russia over its “aggressive and destabilising” actions in Ukraine.
The PM said she is “sure” they will agree on the importance of pushing Russia in response to the “drastic deterioration” in the humanitarian situation in eastern Ukraine.
Mrs May highlighted “vital” cooperation on security and defence and said in the wake of “horrific” terror attacks over the past two years, Britain will “continue to stand shoulder to shoulder” with France “as a staunch ally and a great friend”.
She 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.”