How can I check if I am insured to drive a car in France

French law provides that damages to others created while using the vehicle have to be covered by compulsory third-party/liability vehicle insurance, no matter who is the driver. This is provided for by article L211-1 of the Code des assurances:

Les contrats d'assurance couvrant la responsabilité mentionnée au premier alinéa du présent article doivent également couvrir la responsabilité civile de toute personne ayant la garde ou la conduite, même non autorisée, du véhicule, à l'exception des professionnels de la réparation, de la vente et du contrôle de l'automobile, ainsi que la responsabilité civile des passagers du véhicule objet de l'assurance.

Note that it even covers non-authorised use of the vehicle (say joyriding). But it does not cover damages to the vehicle itself (only mandatory liability insurance) or to unauthorised drivers (not relevant here). This also assumes that you do not drive the vehicle so often as to effectively be the main driver, for the contract could then be void and you could be found guilty of fraud.

As explained by guillaume31, the contract can also include a special excess clause for other drivers so an accident could become expensive but you can be confident that you are not driving illegally without insurance or on the hook for large liability payments (bodily injury, etc.) So if you find a green sticker on the windshield (with the right dates on it), you can be confident that the vehicle is insured and that this insurance technically covers any driver.

As far as I know, clauses limiting coverage to named drivers are very uncommon in run-of-the-mill insurance contracts, unless your aunt explicitly sought a cheaper “conduite exclusive” insurance contract. In that case, having an accident could also impact your aunt's no-claim benefit.

Also, here are few French phrases that might useful when looking for additional information:

• Assurance au tiers: Informal name for insurance covering damages to third parties (“tiers”)
• Responsabilité civile: Liability, the formal name for the same thing
• Assurance tous risques: Insurance covering other risks than compulsory third-party/liability insurance, like damages to the vehicle itself in a collision, fire, theft, etc.
• Conducteur principal: Main driver
• Conducteur secondaire: Another regular driver who should not drive as frequently as the main driver
• Conducteur occasionnel: Anybody else driving the vehicle (including thieves!)
• Conduite exclusive: A cheaper insurance contract with full coverage limited to named drivers (since denying coverage entirely is not legally possible, this is done through additional excess)
• Franchise: Excess
• Franchise prêt de volant: Special excess if you lend the car to a driver without informing the insurer

Note that most European countries insure the car, not the driver (as in the US). That implies that anyone driving it is insured (if he has a valid license).

You can verify that for France by googling, but if she has the car insured (which you see by 'does it have a sticker on the plate/window'), any legal driver is insured with it.