ok, If I were a French/American girl, here's what I would want for my birthday:
High budget:
-Dinner. Preferably at La Tour D'argent or one of Alain Ducasse's restaurants but if you can't afford that, any Michelin 1 star or 2 star restaruant is good. A homecooked meal is great too if you can cook and can't afford one of those places.
-A long weekend trip to the riviera or one of the wine regions or skiing in the alpes. Really anywhere romantic that the TGV goes to.
Middle Budget:
-nice jewelry, you already gave her a necklace so give her matching earrings.
Low Budget
-walk along the seine, bring a picnic and a bottle of wine.