May's speech, in which she promised that Britain would honour its existing budget commitments until 2020 and proposed new guarantees for the roughly three million EU nationals living in the UK, showed "goodwill", Macron told the French press, noting "advances" and "openings".
But he added, "Before moving forward, we hope to clarify things regarding the treatment of European citizens, the financial terms of the exit and the question of Ireland."
"On two of these three issues [...] openings have been made," Macron said, but he did not explain what they were, saying it was up to EU chief Brexit negotiator Michel Barnier to address these points.
Barnier earlier hailed the "constructive spirit" of May's speech but called on her to give more details on the "concrete implications" of the proposals.
Macron, a committed Europhile, plans to unveil his proposals for the EU at a speech at Paris's Sorbonne University on Tuesday, his office announced on Friday.
The speech to students will come two days after Germany's general election, which are expected to see Chancellor Angela Merkel's Christian Democrats able to form a new government.
Macron has already spoken of his desire to strengthen economic and monetary union, have more social and fiscal convergence and beef up migration policy, among other subjects.