Violence has marred the tournament so far, with large-scale unrest between England and Russia fans ahead of the two nations’ match in Marseille on Saturday.
That resulted in both nations being warned by UEFA that further unrest would lead to the two countries being expelled from the tournament, with the Russian Football Union also being handed a €150,000 fine and a suspended disqualification.
The three Russians were among a group of 43 fans detained while traveling on a bus on Tuesday.
The three men will receive jail terms of 12, 18 and 24 months, and will be banned from entering France for two years.
The remaining fans detained will not receive jail terms. However, 20 of them will be expelled from the country, with the other 20 being released without penalty.
