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."
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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 former Brexit minister Lord Bridges, who resigned from the department in June, said Britain needed to be ready for the scenario where the country crashed out of the EU without a deal.
"What will happen at customs, data, aviation, energy, law? The list goes on and on. I would urge the government to not be too coy about this," he told BBC Radio 4's Today programme.
If the EU senses the UK is not ready to leave without a deal, it would be "captured" at the negotiating table, he said.
Backbench MP Jacob Rees-Mogg criticised the PM's stance on freedom of movement until March 2019, offering the union money, and the role of the European Courts of Justice on Britain.
In her speech, the prime minister suggested there should be a new security agreement and a new model for trade
She said the UK and EU would continue to work together on long-term economic projects and the UK would want to contribute to costs.
When the two-year transition period was up, the UK and EU could move towards a new "deep and special partnership," she said.
By March 2019, neither the UK or EU would be ready to "smoothly" implement new arrangements, Mrs May said, so she suggested current trade terms should remain in place.
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