It looks like this pass isn’t valid for travel via any other country,

https://assistance.passefranceallemagne.fr/en/support/solutions/articles/103000121224-which-countries-can-i-visit-

Where is the station you want to transfer? I guess Basel.

Basel SBB is the official France/Switzerland border point (as is Geneva) and Basel Bad Bf is the official border point with Germany.

You should buy a ticket between the two but otherwise you should be good to go.

3.60 CHF full-fare ticket valid for an hour on trains, trams and buses. A good place for a break ! :)

You cannot transfer through Belgium for sure.

Thank you for your replies. 

The train from Mulhouse goes to Basel SBB and the train to Mannheim also goes from Basel SBB though.. so you think I might have problems? Because my rail planner app displays a ticket for the whole journey Lyon- Munich.

To be sure you should buy a ticket for the short hop from Basel SBB (end of France) to Basel Bad Bf (start of Germany). Afterwards the pass is definitely valid.

It should also be possible to go via Strasbourg and take the regional train across the border to Offenburg (to avoid the cross-border TGV/ICE, for which you are entitled to free reservations btw!). The TGV Lyon - Mulhouse should also be free, visit a SNCF ticket counter to get the free reservation.

I'd suggest making a break in Basel anyway. There are hourly ICE trains towards Mannheim and reservations are optional so you've got flexibility. Go to the front/rear end to find more seats.

EDIT : there is a daily Lyon - Mannheim - Frankfurt TGV. What is your travel date ? If it isn't full I'd suggest taking it (free reservation at a SNCF ticket counter).

- TGV Lyon Part-Dieu - Mannheim Hbf 10:04 - 15:18 0€ au guichet (17€ en ligne sinon)

- ICE Mannheim Hbf - München Hbf 15:48 - 18:47

I suggest you create two separate trips in your planner.

Lyon - Basel SBB

Basel Bad - Munich

You can buy the €3.60 ticket that @thibcabe suggested from a ticket machine at Basel SBB, or buy it online in advance. That will be valid for the first few minutes of the train from Basel SBB, then your pass will be valid once the train has reached Basel Bad. You don’t need to get off the train.

Thank you!

Someone from Interrail answered me and said transfer through other countries including Switzerland wasn't possible with this pass. 

I found another journey through Strasbourg than I can do.

I want to travel overnight, that's why it's more complicated.