Let's remember, first, that
we have enough evidence now to point that American gold was used in spanish coinage since the XVIIth century only, and the american gold get directly hoarded by Italy and Netherlands bankers.
The Spanish economy inflation is more issued from its hegemonic policies in Europe and how costly it was from one hand, and then the commercial aspiration that the support of the aforentioned bankers created from the other hand, rather than American gold itself (sorry for the proponents of ironical History).
It can be roughly summarized as "Living too much on its successes and too prone to fall when circumstances were disfavourables. After all, why reform when all goes well? And once it goes bad, well.."
Now, assumng that early Modern France takes the lead on Mexico and Peru*, you'd have some similar issues but not the exact same ones : early Modern France is both more and less advanced bureaucratically than early Modern Spain (more royal power on
pouvoirs régaliens; less so on administrative and peripherical regions); and wouldn't get the same ammount of financial support that Habsburgs did thanks to their huge dominion.
That said, let's remember that early Modern France did relatively well on its own, face to Habsburgs that were blostered by huge financial assets (more from Europe than Americas, at least in the first half), up to the point being able to turn the Italy's Wars into a war of attrition. So, I'd wonder how much Valois would have to rely on American mining and trade on this regard :
you'd probably see a more conserative take on this which would mean that an important part of American minings benefit would be lost for the French crown and going more to french magnates, bourgeois or traders; rather than what happened for Habsburgs.
*It's incredibly unlikely to ever happen, tough. But that's not the matter at hand.