Depends on the Route 

As the Eurail Francepass is valid just on the French Network Luckily Geneva is the border station between France/Switzerland and you can reach it for Example with the TER from Lyon to Geneva :)

As far as I know you need to enter the journey manually and place Geneva in France in order to get this to work. 

Thank you very much for your response :) Do you mean adding the journey (ex Chamonix → Geneva, Geneva → Lyon) onto my Eurail mobile pass?

Thanks for the screenshot. It seems they did fix the bug with Geneva since you didn't have to add your journeys manually.

Thank you so much for your prompt response.

Based on my screenshot, am I good to go from Chamonix to Geneva, and Geneva to Lyon with my Eurail France Pass with no additional payment or seat reservation? :)

Seat reservations are not possible for TER trains (except TER NOMAD in north France).

I am not sure about the TER Annemasse-Geneve. Because on this line the border station is Genève Eaux Vives, this station is some stations before Geneva (Cornavin - Main Station).

And Geneva is also a border station for the line to Lyon. From there to Lyon is it ok. But I am not sure about the TER Annemasse-Geneve.

Or am I here overthinking? 

Seems like a very strange routing to me-the normal route would be avoiding GNV-perfectly possible, as there are direct trains Annemasse-Bellegarde. Normal SNCF-ticketing would also lead via that way. Via Gnv there is a special 2-pounctry combined fare-system, as Swiss charges even more as FR does.

What would be the possible route from Chamonix to Geneva with France pass with transfer?

You have to take the same trains like you planned till Annemasse. From there you take the TER to Bellegarde and from there the TER to Lyon. With this routing you arrive in Lyon 2 hours earlier.

Or do you want to visit Geneva? In this case just ask the train staff at Annemasse, there the trains change staff from French to Swiss. They can tell you if it is ok to go via Geneva. 

You have to take the same trains like you planned till Annemasse. From there you take the TER to Bellegarde and from there the TER to Lyon. With this routing you arrive in Lyon 2 hours earlier.

Or do you want to visit Geneva? In this case just ask the train staff at Annemasse, there the trains change staff from French to Swiss. They can tell you if it is ok to go via Geneva. 

Yes, I wanted to stopby Geneva for few hours. So it is not possible to go to Geneva via my screenshoted route with France pass? Would there be any other possible route to get to Geneva from Chamonix?

I don’t think it is possible. But you could ask via Social Media to SBB directly if you can use the Eurail Pass France on the line between Annemasse and Geneva. Or you look how much it would cost for this short trip. Maybe you have to pay only Genève Eaux Vives to Geneve.

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You have to take the same trains like you planned till Annemasse. From there you take the TER to Bellegarde and from there the TER to Lyon. With this routing you arrive in Lyon 2 hours earlier.

Or do you want to visit Geneva? In this case just ask the train staff at Annemasse, there the trains change staff from French to Swiss. They can tell you if it is ok to go via Geneva. 

Yes, I wanted to stopby Geneva for few hours. So it is not possible to go to Geneva via my screenshoted route with France pass? Would there be any other possible route to get to Geneva from Chamonix?

Thank you so much. I’m truly learning a lot today :)

Summing it up, I can use my France Pass from Chamonix to Annemasse.

Then pay for the ticket from Annemasse to Geneve.

Then use my France Pass from Geneve to Lyon

Am I correct??

Yes Charmonix to Annemasse is clear (it is in France), Annemasse-Geneve you found a solution and Geneva-Lyon is included in the Pass for France.

You are good to go. Have fun. 

Well, actually, your pass for France is valid until Genève-Eaux-Vives, so a ticket is only needed between Genève-Eaux-Vives and Genève, costing CHF 3 instead of CHF 4.90 from Annemasse.