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For clarity, Switzerland is not in the EU. However, for obvious reasons, Swiss police are very familiar with the format of EU licences, and Swiss licences have a very similar format.
While there may not be an explicit law about it, I think it would be logical that if she has a French driving licence, she should show this one if it is required by a French official. Local driving licence holders may get slightly better treatment: It's often reported that foreign drivers in France who are pulled over for an infraction are required to pay fines on the spot or have their car impounded due to the difficulties in enforcing penalties internationally.
Therefore, if she is required by an official to show her licence in France or Switzerland, she should show her French one.
However, car rental staff are not officials. There's no legal requirement that you show car rental staff the same drivers licence as you would show a police officer if you are pulled over. She can show the car rental staff her American licence if she wants.