At least four exceptions could be invoked.

1. Unacceptable punishment. This could certainly be invoked, since Snowden faces Espionage Act charges. The current charges don't carry the death penalty, but the possibility of further charges might be raised. But as with Assange, it wouldn't bar extradition; the US simply agrees not to seek the death penalty and then the process continues. Solitary confinement could also arise here.

2. Lack of dual criminality: the Espionage Act is extraordinarily broad, and I don't know whether France's espionage/treason laws are comparable. But since Snowden faces theft and computer charges which have clear dual criminality, I don't know how this would proceed. The US might have to agree not to pursue Espionage Act charges, but you'd have to ask a lawyer.

3. Unfair trial: this is subjective, and not covered by the US/France extradition treaty. The European Court of Human Rights has stated that a merely unfair trial is not a bar, and requires a "flagrant violation of human rights", but France could potentially apply a narrower standard. And while unfair trial isn't a basis to reject a US extradition, it is a basis to grant asylum, which would take legal precedence.

There is a good candidate here: the Espionage Act bars any question of whether the information was justifiably secret, bars defendants from introducing key evidence in their defense, bars the defendant from discussing their intent, and doesn't require proof of real or even potential harm to convict. France could argue that Snowden faces conviction over harm which was both unintended and impossible in the course of exposing an illegal action.

Of course, this would again be moot if the Espionage Act charges were dropped (although not if asylum was granted first). And it could be tough both legally and politically depending on how France's most secretive prosecutions are structured.

4. Politically motivated charges: this both grounds for asylum and a treaty bar to US/French extradition. It's also incredibly subjective, so it certainly could be invoked by a French court.

Snowden's actions don't fall under any of the explicit categories for which political extraditions are required (those are things like attacking diplomats). The US could argue they fall under the "serious harm" clause, but that's neither clearcut not an actual requirement to extradite. (It merely must be taken into account by the surrendering nation.)

France isn't terribly likely to claim this, since the programs and agencies Snowden exposed generally align with French intelligence interests. But a court probably wouldn't have much trouble justifying the finding: Snowden exposed embarrassing actions like spying on foreign heads of state (including France!), US judges have said some of the exposed programs are probably unconstitutional, and he contradicted official testimony to Congress. Combined with a charge that explicitly excludes defenses of public interest, government error, or harmless action, it would be easy to argue the US is using the trial to prevent scrutiny of political misbehavior.

None of that is going to happen, obviously, and I'm not taking a stance here on whether it would be correct. But there's at least one extradition bar which could be easily invoked and justified if someone decided to do so.