The man, identified by French media as Gregoire Moutaux, 25, was arrested on the Ukrainian border with Poland.
Intelligence chief Vasyl Hrytsak said the man had planned 15 attacks and was driven by ultra-nationalist views.
Ukrainian agents had been following the man since December, and allowed him to buy five machine guns, two rocket-propelled grenade launchers, 125kg of TNT, 100 detonators and other arms. He also bought 20 balaclavas before he was arrested at the Yahodyn border crossing between Ukraine and Poland last month, the Ukrainian Security Service said.
The intelligence agency, known as the SBU “has managed to foil a series of 15 terrorist attacks which were planned to target France before and during” Euro 2016, said Mr Hrytsak.
Ukraine officials did not identify the man but said the suspect wanted to protest over his government’s migration policies and the spread of Islam. It said he planned attacks on bridges, railways and other infrastructure for the Euro 2016.
The Paris prosecutor’s office, which handles terrorism cases at a national level, said no investigation had been opened. France’s foreign ministry confirmed the arrest in Ukraine.
Extremist attacks are a major concern for French authorities at the month-long tournament at stadiums in the Paris area and eight other cities which starts this Friday. French officials have already said they are deploying a 90,000-strong security force for the tournament.
A French newspaper identified the man as Moutaux and said investigators raided his home in Nant-le-Petit near the eastern city of Nancy at the end of May. French television network M6 reported investigators found T-shirts promoting an extreme right group.
Ukrainian authorities released photos of a fair-haired man, with his face blurred, holding various weapons,as well as a video of the arrest which showed special forces officers dragging the man out of a van.
The Frenchman arrived in eastern Ukraine last year and was “trying to establish ties with Ukrainian troops under the guise of volunteering,” the Ukrainian agency said.
Senior police officials in France said security measures tested since the November attacks in Paris that killed 130 victims have been adapted for Euro 2016.