Macron, who has expressed impatience over repeated postponements of the deadline for Britain's departure from the European Union, made the remarks as he hosted the new president of the European Council, Charles Michel, at the Elysee presidential palace.
“We must be able to move forward quickly” after Thursday's election, he said.
Twenty-seven European Union leaders — all minus Boris Johnson — will meet in Brussels on Thursday and Friday to discuss Britain's pending departure from the union, the subject of years of fraught negotiations between London and Brussels.
“In any event, it will be very important to stick with the method followed until now, that is to say unity of the 27, (EU Brexit negotiator) Michel Barnier alone conducting negotiations, rigour in defending our interests without yielding to pressure and while respecting, with Britain, the conditions of fair competition,” said Macron.
Britain has until January 31 to leave the EU, after having obtained three postponements.
Michel underlined the importance of building “a close relationship with Britain” after Brexit, calling it “an extremely important partner for the European Union”.
This week's talks will focus on the EU's post-Brexit ties with Britain, particularly regarding trade.
Also on the agenda is the EU's budget, with Michel urging leaders not to dig in their heels, but instead “move forward to bring different points of view closer together.”
“We need more political debates,” in the European Council, “without taboos”, said Macron.
The future budget must reconcile the financial loss from Britain stopping its contributions with new priorities such as climate change, security, and defence concerns, on top of existing commitments such as agriculture.