Geneva airport -- Drop off on French side, then picku up on Swiss side

I'm traveling by car, first in France and then Switzerland. To avoid one-way car rental fees, I was wondering about the idea of two rental periods. The first rental would be in France, ending at the Geneva airport. I could then walk to the Swiss side and begin a new rental there, ultimately dropping off the car in Zurich. Is this feasible, or are there problems I'm not anticipating? Thanks!

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