Billionaire Elon Musk is set to meet French President Emmanuel Macron in Paris on Friday as part of a European trip, with national leaders jostling for investment from his electric car firm Tesla.

The maverick tech titan, who also owns SpaceX and Twitter, met Italian Prime Minister Giorgia Meloni on Thursday, and she later tweeted that they had a "fruitful meeting" discussing "innovation and opportunities".

Macron confirmed during a visit to France's biggest technology trade fair VivaTech earlier this week that he would meet the businessman to "tout the attractiveness of France and Europe".

Musk will also visit VivaTech later, appearing before an audience of thousands for what is billed as an hour-long "conversation" with the event's French founder Maurice Levy.

Musk and Macron held talks in May and afterwards he said he was considering big investments in France.

The country's technology minister Jean-Noel Barrot fuelled speculation earlier this week by telling US broadcaster CNBC that "a lot of effort and energy" had been expended to secure a Tesla factory for France.

But reports from Spain have claimed that Tesla is planning to build a factory there.

The electric carmaker's European footprint is relatively small, having opened its first manufacturing plant in Germany last year.

Awkward interviewee 

Macron gave details of his intentions during a walk around the aisles of VivaTech on Wednesday.

"We're going to talk about artificial intelligence, where he is involved, social networks and regulatory frameworks," he said.

"I'm also going to talk to him about cars, batteries and the sector, to tout the attractiveness of France and Europe."

Europe's leaders and plutocrats are desperate to get some face time with Musk -- in Paris he will meet French fashion magnate Bernard Arnault, with whom he regularly trades the title of "world's richest man".

But despite the breadth of Musk's business empire -- his brain implant firm Neuralink recently got US approval to start human tests -- it is his acquisition of social media network Twitter that continues to fascinate and baffle observers.

He bought the platform for $43 billion, sacked much of its staff, allowed right-wing conspiracy theorists to return and introduced all sorts of fees and charges.

He admits the platform is no longer worth anywhere near the amount he paid.

Maurice Levy, who will interview him in an auditorium that holds more than 4,000 people, said Twitter would certainly be on the agenda.

But Musk is a notoriously tricky interviewee, prone to lengthy pauses, off-topic rambles and making coded references to sex and drugs.

Levy said he would try to rise to the challenge but told French broadcaster BFMTV he could not pretend to be a journalist.

"I'm not looking for a scoop, I'm looking for an explanation, I'm looking to understand," he said.