Franky Zapata, the creator of the Flyboard Air, which can fly for more than 2,500 metres (8,000 feet), said the intervention was typical of French bureaucrats' attitude to innovators.
France has long suffered from a reputation for bureaucractic heavy-handedness that stifles business, something that some of the candidates for next month's presidential election have vowed to tackle.
Former professional jet-ski pilot Zapata told AFP that after flying the Flyboard Air for almost a year he had been summoned to a police station and told he needed registration and a licence.
“We informed the authorities, everyone told us we were in a legal grey area but the approval process was under way,” he said.
Prosecutors in the southern town of Aix-en-Provence said on Tuesday they had opened a preliminary enquiry into “failure to respect overflight regulations and operating an aircraft without the necessary paperwork”.
The Flyboard Air uses powerful jets of air to fly over water and last year Zapata set a new Guinness World Record for the furthest hoverboard flight, when he cleared 2,252 metres — smashing the previous best of 275.9 metres.
But he said he was now thinking of taking up offers to relocate abroad — he has had several invitations, in particular to move to the United States.
“I've always been afraid to go abroad with my technology but now I'm asking myself the question,” he said. “
“They've told me I have two months to comply with the rules, but there are no rules, they have to be written, I'm completely lost.”
In a Facebook post on Friday, liked over 150,000 times, Zapata said his treatment was symptomatic of France's attitude to innovators.
“While the rest of the world is making us offers to relocate, I'm not wanted in my own country!” he wrote.
“I feel sick for the wasted potential in my country. Reluctantly, I'm going to have to leave France.”
Before the Flyboard Air, Zapata invented the Flyboard, a hoverboard that connects to a jetski and flies by jets of water. Skilled riders can execute spectacular flips and spins and the inaugural world championships were held in Qatar in 2012.
Zapata said he was particularly disgusted by his treatment after “making more than 10,000 Flyboards in France”.
Aix deputy prosecutor Emmanuel Merlin said residents in the town of Martigues had complained about noisy flights near residential areas, adding “you can't fly just anywhere, especially near an airport”.
A civil aviation spokesman said Zapata had not respected safety rules and should take a “navigator's theory exam”, in line with drone and microlight pilots.