Macron said he was "deeply sad" while EU's Guy Verhofstadt pledged to try and "ensure the EU is a project you'll want to be a part of again", the BBC reported.
Celebrations and anti-Brexit protests were held on Friday night to mark the UK's departure.
Ex-Brexit Secretary David Davis said everyone would be a winner in the end.
The UK officially left the EU on Friday at 11 p.m. after 47 years of membership, and more than three years after it voted to do so in a referendum.
Brexit parties were held in some pubs and social clubs as well as in London's Parliament Square, as the country counted down to its official departure.
In Scotland, which voted to stay in the EU, candlelit vigils and anti-Brexit rallies were held.
In a message released on social media an hour before the UK left, Prime Minister Boris Johnson vowed to bring the country together and "take us forward".
"For many people this is an astonishing moment of hope, a moment they thought would never come," he said. "And there are many of course who feel a sense of anxiety and loss."
In an open letter to the British public, Macron said he was thinking of the millions of Britons "who still feel deeply attached to the European Union".
"You are leaving the European Union but you are not leaving Europe," he said. "Nor are you becoming detached from France or the friendship of its people.
"The Channel has never managed to separate our destinies; Brexit will not do so, either."
Macron also said the EU must learn lessons from the "shock" of Brexit, adding: "I am convinced therefore that Europe needs new momentum."
And he defended the way France acted in the Brexit negotiations, saying neither the French nor anyone else in the EU was "driven by a desire for revenge or punishment".
Meanwhile, the EU Parliament's Brexit coordinator Verhofstadt responded to a message which had been projected onto the White Cliffs of Dover by a pro-EU group.
"We will look after your star and work to ensure the EU is a project you'll want to be a part of again soon," he said.
Speaking on BBC Radio 4's Today programme, Davis - who quit as Brexit secretary in protest at former prime minister Theresa May's Brexit plan - said it would be a "fair race" to reach a trade deal with the EU by the end of 2020 but "it can be done".
The UK is aiming to sign a permanent free trade agreement with the EU, along the lines of the one the EU has with Canada, by the end of the transition period in December.
Davis said reaching a deal was "not a charitable exercise, this is an exercise of both sides recognising their own best interests".
European leaders have warned that the UK faces a tough battle to get a deal by that deadline.
Mairead McGuinness, the vice president of the European Parliament, said progress to agree a trade deal "might be left to the very last minute".
"Normally in trade negotiations we're trying to come together," she told BBC.
"For the first time we're going try and negotiate a trade agreement where somebody wants to pull away from us. I can't get my head around that and I think it's going to be quite complicated."
Thousands gathered in Parliament Square to celebrate Brexit on Friday night, singing patriotic songs and cheering speeches from leading Brexiteers, including Nigel Farage.
The Brexit Party leader said: "This is the greatest moment in the modern history of our great nation."
Pro-EU demonstrators earlier staged a march in Whitehall to bid a "fond farewell" to the union.
Police in Whitehall arrested four men and also charged one man with criminal damage and being drunk and disorderly, while in Glasgow one man was arrested.
Meanwhile, other symbolic moments on a day of mixed emotions included:
* The Union flag being removed from the European Union institutions in Brussels
* The Cabinet meeting in Sunderland, the first city to declare in favour of Brexit when the 2016 results were announced
*A light show illuminating 10 Downing Street and Union flags lining The Mall
* A 50p coin to mark the occasion entering circulation
* The building of the UK government's delegation to the EU changed its name and sign
Meanwhile, US Secretary of State Mike Pompeo said he was "pleased" the UK and EU had agreed a Brexit deal and the US would continue to build its "strong, productive, and prosperous relationship with the UK".
Washington's ambassador to the UK, Woody Johnson, said Brexit had been "long supported" by US President Donald Trump.
( With inputs from IANS )