Tolls cost when driving from Switzerland to Chamonix

From where, exactly, in Switzerland?

I'd recommend using Via Michelin to assess the cost of tolls and fuel, based on your vehicle type.

does your car have a Swiss Vignette?

A second to Bob's recommendation to use Via Michelin - it will give you the exact cost for all tolls on any given route.

we really need to know where in Switzerland you are starting because some French roads have tolls and some don't, and the tolls vary.

Will the car be rented in France or Switzerland?

€110 sounds like an exotic routing by Rome 2 Rio and is very inflated, depending on the previous answers.

Please come back with more detail, including the fuel of the car.

If you take the road from Martigny to Chamonix, you do not pay any French tolls. You just need the Swiss Vignette (49 francs IIRC) to drive in Switzerland, if your car does not come with it.
This would be the most logical way to arrive, unless you are coming from Geneva & lakeside towns south of Rolle (from where you'd use the French A40) or from Ticino & southern Graubünden (from where you'd drive through Italy and the Mont Blanc tunnel). It is scenic, and the road is not scary IMO.