- Video report by ITV News Political Correspondent Libby Wiener
In a press conference in Paris, both leaders expressed a willingness for the UK to leave the EU with a deal, and Mr Macron backed Angela Merkel's call for the UK to come forward with proposals within 30 days.
"What Angela Merkel said yesterday and which is very much in line with the discussions we have had since the very beginning is that we need visibility in 30 days," he said.
He said the EU's negotiator Michel Barnier could be involved in finding an answer "without totally reshuffling the Withdrawal Agreement".
"We should all together be able to find something smart within 30 days if there is goodwill on both sides."
However on Thursday Mrs Merkel sought to play down the importance of the 30-day period she had floated on Wednesday, saying it was merely "an allegory for being able to do it in a short period of time".
Speaking to reporters in the Netherlands she said that "it would be better to say one can achieve that by October 31".
- ITV News Correspondent Angus Walker says there is a "sense of optimism" from Downing Street following the two meetings, but the "fundamental positions" of France and Germany have not changed and there is "little room for manoeuvre" for Boris Johnson.
After meeting Mr Macron, Mr Johnson tweeted: "Today I met President @EmmanuelMacron in Paris. Let's get Brexit done, sensibly and pragmatically and in the interests of both sides. Let's get on with deepening and intensifying the friendship and the partnership between our nations."
And Mr Macron tweeted: "The relationship between the United Kingdom and France is, in my eyes, essential and unalterable. @BorisJohnson, I see in your choice to come to Paris the need to maintain this privileged relationship. Let's work together!"
Mr Johnson said while he wants a deal, the UK "must come out of the EU on October 31 - deal or no-deal".
The prime minister believes the only way a deal with the EU would be approved by Parliament, is if he can remove the backstop - the contingency plan to remove any need for a border in Ireland.
He insisted alternatives to the backstop could be found as "where there's a will, there's a way".
However the French president told Mr Johnson the Withdrawal Agreement and Irish backstop are "not just technical constraints or legal quibbling" but are "genuine, indispensable guarantees" to preserve stability in Ireland the integrity of the single market.
But he said the EU had "always said that it was available to discuss, depending on the wishes of the UK, our future relationship".
Labour leader Jeremy Corbyn echoed Mr Macron's comments on stability in Ireland.
He said: "The question of the Irish border is fundamental to a lot of things. The Irish peace process was an enormous step forward. It's an international treaty, it's an international agreement.
"It cannot be negotiated away by Boris Johnson or anybody else so I think President Macron is quite right to say they're not going to allow a hard border to return in Ireland and I'm absolutely with him on that."
Mr Johnson was asked by ITV News Political Correspondent Libby Wiener on what leaving without a deal actually means.
He said: "A great deal of work has already been done to ensure that the transition on October 31st is as smooth as it possibly can be and so there are already agreements on aviation, on many other sectors."
He added: "What we want to do now in the next 71 days or whatever is remaining, we want to make sure that we do all the necessary work on both sides of the Channel to make sure that whether we get an agreement or not, our exit is as smooth and as pain free as possible."
Following the meeting the EU's chief Brexit negotiator, Michel Barnier, ahead of a meeting with European Council President Donald Tusk, said "no-deal (Brexit) will never be the choice of the EU".
He said: "I am now meeting now meeting President Tusk as we do regularly. I always say that the EU prefers an orderly withdrawal of the UK respecting the single market, the integrity of the single market, and obviously the peace and stability in Ireland. I just want to add that the no-deal (Brexit) will never be the choice of the EU, never."
It comes after Mr Johnson met German leader Angela Merkel in Berlin for Brexit discussions.
Mrs Merkel, in a joint press conference with Mr Johnson, hinted it was possible within 30 days, despite skepticism that a deal can be achieved and approved by Parliament within the timetable.
She said: "If one is able to solve this conundrum, if one finds this solution, we said we would probably find it in the next two years to come but we can also maybe find it in the next 30 days to come."
Mr Johnson welcomed her “blistering” suggestion, claimed there are "abundant solutions" to the backstop, and said the "onus is on us" to find them - but did not mention any specifically.
He said: "I think what we need to do is remove it whole and entire - the backstop - and then work, as Chancellor Merkel says, on the alternative arrangements."
Mr Johnson is expected to meet US President Mr Trump at the G7 summit in Biarritz which starts on Saturday, but Mr Macron warned that the UK would be a "junior partner" in its relationship with Washington after a hard Brexit.
Following their press conference, Mr Johnson and Mr Macron had lunch in the Elysee Palace before going for a walk through the gardens together, accompanied only by an official photographer.
The leaders then enjoyed coffee in the palace where there was some small talk between then, although the conversation was inaudible to the travelling press pack.
Mr Johnson left the palace following the coffee and is due to fly back to the UK before conducting domestic visits on Friday.