"We had a good start, very active with a lot of chances," the much-travelled former NHL player told reporters. "In the second period, we got some more goals and I think from that point on we controlled the game."
The Slovaks registered 24 of their 37 shots in the first two periods, scoring three goals in the process to take command.
Beaten finalists in 2012, Satan's side scored a further two goals to go 5-0 up in the third. The French pulled two back but never really threatened before Libor Hudacek finished the scoring late on.
With the tournament once again being co-hosted by Finland and Sweden, the Finns had a narrow escape as they overcame Germany 4-3 after overtime. Their co-hosts were not as fortunate, slumping to shock 3-2 defeat by Switzerland in Stockholm.
"That's not how we wanted to start the tournament," Sweden's goaltender Jacob Markstrom told reporters. "It's too bad. It didn't hold up today. We weren't good enough."
In the other game in Stockholm, the Czech Republic beat Belarus 2-0 as Czech goaltender Alexander Salak, who plays in the Sweden's Elitserien for Farjestad, kept a clean sheet on his world championship debut.
Defending champions Russia make their bow on Saturday when they play Latvia, with the United States facing Austria and Canada taking on Denmark.