Macron hailed May for “courageous work” in seeking to implement Brexit in the interests of her country and with respect for Britain's European partners, the Elysee said in a statement.
But it added: “The principles of the EU will continue to apply, with the priority on the smooth functioning of the EU, and this requires a rapid clarification.”
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Macron and May's strained relationship was the subject of a piece by French street artist Combo. Photo: AFP
The British Prime Minister announced on Friday that she would step down on June 7th, following huge pressure from within her own party.
During her premiership she has frequently been at loggerheads with Macron, who has taken a tough line on the UK's repeated requests for extensions to the Brexit deadline.
The Elysee's statement said that while France was ready to work with Britain's new prime minister, “it is too early to speculate over the consequences of this decision” by May to step down.
Since the first Brexit deadline of March 29th was missed, Theresa May has twice had to go to Europe and request extensions and on her last trip it was Macron who took the toughest line against it.
Despite the EU granting a further extension until October 31st – the current deadline – France has continued to warn that there can be no further delays.
“We must not get sucked into repeated extensions, that's for sure,” a French presidential adviser told the media at the start of this month.
“Our message is clear: a solution must have been found by October 31st.”
The pro-European Macron is said to have become frustrated that Brexit has distracted attention away from his own plans for reforming the way the EU works.
May said she would quit as Conservative Party leader on June 7th and would remain as prime minister in a caretaker role until a replacement is elected by the party.
The leader of the party automatically becomes prime minister. Her plan to leave the European Union with a deal she thrashed out with Brussels had been repeatedly rejected by parliament.
A crowded field is expected to contest for the leadership, with hardline Brexit supporter and former foreign secretary Boris Johnson making no secret of his ambitions.
The Elysee warned: “At a time of an important choice, votes of rejection that do not offer an alternative project will lead to an impasse.”
Johnson has repeatedly said Britain should not fear a so-called no-deal Brexit.