The UK must provide more clarity about its negotiating position on Brexit, the French president has said.
Emmanuel Macron said the issues of EU citizens' rights, the exit bill and the Irish border question must be settled before talks could be held on trade.
On Friday, Theresa May made suggestions including a two-year transition period after Brexit, and that the UK pay the EU for "commitments" previously made.
She hoped this offer, made in a speech in Italy, would unblock Brexit talks.
In the first response by a European leader to the speech, Mr Macron welcomed her initiative, but said the British position still needed to be fleshed out.
"Before we move forward, we wish to clarify the issue of the regulation of European citizens, the financial terms of the exit and the question of Ireland," he said.
"If those three points are not clarified, then we cannot move forward on the rest."
Mrs May said there should be a transition period of "about" two years after March 2019 - when the UK leaves the EU - during which trade should continue on current terms
EU migrants would still be able to live and work in the UK but they would have to register with the authorities, under her proposals.
And she said the UK would pay into the EU budget for decisions made while it was a member, so other member states were not left out of pocket.
'We have not left'
She did not specify how much the UK would be prepared to pay during the transition period, but it has been estimated as being at least 20bn euros (about £18bn).
Mrs May's speech was welcomed by senior Conservative figures including Foreign Secretary Boris Johnson and Chancellor Philip Hammond.
But backbench MP Jacob Rees-Mogg criticised the PM's stance on freedom of movement - saying it should end in March 2019 - offering the union money, and the role of the European Courts of Justice on Britain.
He told BBC Newsnight it was a "red line" if the UK was still subject to the ECJ after March 2019. If it was, "we have not left the European Union", he said.
The prime minister, in her speech, also suggested a "bold new security agreement" and said the UK would be the EU's "strongest partner and friend".
On trade, she said the two sides could do "so much better" than adopt existing models, adding there was "no need to impose tariffs where there are none now".
She also suggested that the UK and EU would continue working together on projects promoting long-term economic development and the UK would want to "make an ongoing contribution to cover our fair share of the costs involved".
When the two-year transition period was up, the UK and EU could move towards a new "deep and special partnership," she said.
But by March 2019, neither the UK or EU would be ready to "smoothly" implement new arrangements needed so suggested current trade terms should remain in place.
Such a period should be "time limited", she said, with its length being determined by how long it takes to set up new systems.