In a bid to restart stalled negotiations, the Prime Minister set out her vision to continue paying the EU for a two-year transition period after Britain leaves the bloc in 2019.
But Mrs May's speech, delivered in Florence, failed to move French president Mr Macron.
He said more progress was needed over issues such as EU citizens rights in Britain, the Irish border and divorce settlement before talks over matters like trade could continue.
Pro-Brexit Tories have now criticised Mr Macron, accusing him of being unreasonable in demand such detail at this stage of negotiations.
Following Mrs May's speech, the French leader welcomed her "willingness" to make progress and sort out the future relationship.
But he said: "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."
His stance was echoed by Brussels' chief negotiator Michel Barnier, who said Mrs May's assurances needed to be translated into a "precise negotiating position".
On Saturday, Conservative backbencher Bernard Jenkin said Mr Macron was asking for too much too soon.
"How can we put money on the table when we don't know what the deal is?" he said.
"How can we discuss how the finer details of the Northern Ireland border should operate when the EU won't even begin to discuss what the relationship is that they want between the UK and the EU?"
Under Mrs May's proposals, the UK could pay around £18 billion into the EU budget during the transition period - enabling access to the single market.
EU nationals would also remain free to move to Britain, although they would have to register with the UK authorities.
Czech Europe secretary Ales Chmelar warned the final divorce settlement would be much higher than £18 billion.
"This is just a payment for the remaining financial framework period," he said.
"This is not a payment for all the legacies that we see including for example the pensions and the legacies in terms of grants and funds."
Conservative peer Lord Bridges, who quit in June as a Brexit minister, said the Government needed to be prepared for the possibility talks would fail, resulting in Britain leaving the EU without a deal.
"I would urge the Government not to be too coy about this. It is absolutely the case that we need to be ready for that," he said.
"If we are not ready for it and the EU senses we are not ready for it, we will be captured at the negotiating table.
"It is in our interests to do a deal, it is in Europe's interests to do a deal. But at the same time we need to be ready."