Belgian railways also sell reservations for this train (but not online) and publish their conditions online.  They say: 

Beneficiary

Adults in possession of a valid Eurail or Interrail pass validated for the day of the journey, covering at least the French part of the journey.

See:
https://public-pf.b-europe.com/en/Producten/Details?id=cb2dc856-d565-417e-bcfd-2e8ab7132f73

They don't make that up, SNCF must have told them.

Hi thibcabe, are you 100% sure that one can also travel to Milano Porta Garibaldi only having a One Country Pass valid for France? I’m contemplating using this TGV service and I’d like to be 100% sure. Did you already travel yourself using only a One Country Pass for France?

It is really hidden on the website but here's what you're looking for : 

Train stations of bordering countries

An Interrail Pass valid in France covers travel to some train stations of bordering countries:

• Basel (Switzerland)

• Geneva (Switzerland)

• Portbou (Spain)

• Ventimiglia (Italy)

https://www.interrail.eu/en/plan-your-trip/tips-and-tricks/trains-europe/trains-country/trains-france#tabs-da0dadc90f-item-e60edbc8d3-tab (under high-speed trains)

Hey, 

are there any other such connections that are covered by a France One Country Pass (like, for example traveling from Nice To Ventimiglia on a french TER)?

Thanks! 

The one-country pass is valid on the TGV until Torino Porta Susa or Milano Porta Garibaldi. The former has easier connections to Florence, otherwise you may have to transfer at Milan (subway/walk).

Remember that you have to pay a 30€ seat reservation for the cross-border TGV (so an advance ticket on the direct Frecciarossa may be cheaper, do check).

You can't take the direct Frecciarossa to Milan (not included whether you have a global pass or a one-country).

Your itinerary will be :

- TER Lyon Part-Dieu - Chambéry

- TGV Chambéry - Turin/Milan

- Frecciarossa Turin/Milan - Florence own ticket