Boris Johnson wants a modern recreation of the Roman Empire as a way of achieving co-operation between Europe and its neighbours.
Mr Macron said the Prime Minister was interested in his political community vision when the pair met at the G7 summit in Germany, but Mr Johnson said he wanted a wider grouping.
The French President wants his political community to allow the EU to force closer ties with non-members, such as the UK and the nations of the western Balkans.
But Mr Johnson told reporters accompanying him at the Nato summit in Madrid he had a vision based on the Roman “Mare Nostrum” – the Mediterranean Sea and the countries around it.
“Emmanuel has an idea, which I actually claim paternity of this idea,” Mr Johnson said.
“I had this idea back when I first became foreign secretary. My view is that we should rebuild the whole concept of … so I think that Turkey should be there, I think that Maghreb should be there, and I think we should basically be recreating the Mare Nostrum of the Roman Empire.
“That’s basically what I think. Of course Ukraine, Turkey, Maghreb, there’s got to be a role for all of us in a wider conversation about issues that affect all of us.
“I think possibly what’s going on here is that there are several different ideas.
“That doesn’t mean that they are necessarily all the same.
“I think possibly rather than inventing new structures, let’s look at building up relationships.”
Asked whether he would give a yes or no to Mr Macron’s plans, the Prime Minister said: “In so far as it is compatible with some of the things that I have been talking about just now it is worth looking at.
“There’s a role for… I think Turkey is crucial. I think the North African littoral is also a very important area for the wider European debate. Israel. Come on.”
Mr Johnson’s interest in the geopolitics of the Roman Empire could stem from his Oxford University degree in classics.
He frequently drops Latin phrases into his speeches and comments – often causing bemusement in audiences less familiar with the language.
In a more modern reference, he referred to his idea as “Eurovision” – the song contest which has stretched the definition of Europe so far it includes Australia.