Anyone who goes on the track is at serious risk of electrocution.
Trains were halted and the power was cut at six stations for half an hour on the busy line 9 shortly before midday.
The man fled towards a tunnel as inspectors pursued him along the station platform.
The line is powered by a 750-volt current from a raised third rail.
The man was later caught. It is not clear what action has been taken although travelling without a ticket commands a fine of at least €50 (£43; $55) on the Paris metro.
Video of Monday's incident went viral after it was captured by a man who remarked: "I've seen people flee inspectors but this guy!"
Social media users were incredulous that the man had risked his life to avoid paying for a ticket.
"The metro doesn't run on batteries," said one. "The bloke's prepared to die of electrocution for a ticket that costs €1.90! He should thank the inspectors for saving his life by cutting the power."