The hosts have lost just once since July 2021 and still have hopes of retaining the trophy after hammering England in round four.
Owens' side have won just once this campaign, last Saturday's victory over Italy.
"The pressure is off externally, because no one is expecting anything from us," Owens told reporters.
"There's always added pressure when you're the favourites because generally you have confidence and momentum and that's what comes with being favourites," he added.
Les Bleus claimed a record victory in London last Saturday and can clinch the Six Nations with a bonus point victory at the Stade de France so long as Ireland lose to England later in the day by more than seven points.
"They had a fantastic performance against England last week at Twickenham," Owens, 36, said.
"They will have been revved up, it was their first Six Nations win there since 2005," he added.
Wales' tournament has been marred by off the field issues including allegations of a "toxic culture" at the Welsh Rugby Union with claims of sexism, racism and homophobia made by former employees.
Last month, a player strike over contract problems was cancelled just days before a loss to England, which came after convincing defeats to Ireland and Scotland.
"We know we always have to get better to compete with the top teams in this competition," Owens said.
"We have done so in certain areas and we will have to be at the top of our game on Saturday," he added.
World Cup looming
France have added 147kg prop Uini Atonio and 135kg lock Romain Taofifenua to a pack which dominated England last time out.
"The hardest thing with those boys is that they're big men but they're very athletic, they move well and are fit," Owens said.
"You expect players that size to be slow after 40-50 minutes but that doesn't happen with them.
"When they keep coming you have to get off the line and keep tackling them.
"It takes the energy out of you," he added.
Owens' squad have spent the week in Nice, where they will face Portugal on September 16 in the Rugby World Cup pool stage.
"We had a good performance last week, a good win," Owens said.
"We have to deliver again this week leading into a World Cup preparation for what's to come in the autumn," he added.
