There are non-stop flights between Strasbourg and Calvi on HOP but only once a week in summer, not in April. There are probably a few other seasonal flights to Corsica from either Strasbourg or Basel/EuroAirport. You haven't mentioned Luxembourg but it is not so far away and Luxair also offers several flights between Corsica and Luxembourg in the summer. None of this is going to help in April, though.
Your best bet outside of the holiday season is EasyJet from Basel. They have non-stop flights to Corsica year-round (probably to Ajaccio, not Calvi). Low cost airline flights typically do not show up on regular travel agents/flight aggregators so you might want to check their website directly.
Alternatively, you might also consider taking the train to Paris and fly from there. It might not seem like a logical choice geographically speaking but there are quick train links with some cities in South-West Germany. The train can be pricey as well so all-in-all it might or might not be more attractive than a flight connection in Paris. There are also night trains from Luxembourg or Strasbourg to Nice or Marseille but then you need to add the price of the ferry or flight to the island as well.