SNCF do not provide online booking for interrail passholders.

The only options are through the interrail booking website or b-europe site for domestic French passholder bookings here https://travel.b-europe.com/eurail-ge/en/booking-tgv#TravelWish

Alternatively, bookings can be made at ticket offices and ticket machines at SNCF stations.

Bookings can also be made through SNCF phone booking service although reports are that success is very variable, sometimes it works easily others just get refused due to “foreign bank cards” and other odd reasons. details of the numbers is on the SNCF connect website.

Trains generally don’t book out 3 months in advance or anything like that, of course there will be higher demand for some than others and at certain periods.

All major INland TGV routes have an hourly service and no, this is not OZzieland with the 1/MO Ghan to the Springs-even on the day itself you will find empty seats. No (not now!) worries mate!

Just a hint re this period: perhaps to utter surprise: on 1/5 In FR they do celebrate the victory of the red flag waving workers on those miserable patrons. That means nearly all public services are closed then-to allow those jolly workers to participate. Trains do run, but double check times.

As a surprise they may even hand out little flowers or red candies or the like.

Which connection on which date are you trying to book? I highly doubt it'll book out so soon. Only a bit before or after Christmas holidays that's somewhat of a risk. 

The bookings just opened until 31st of May for inland TGV services. If you try to book a date later than that, just be a bit patient. It'll show up eventually.

@mcadv almost all of Europe celebrates Labour day, not only the French. In fact, almost the whole world. Countries not celebrating it are much rarer... It's just ordinary Sunday schedule, a public holiday like many others.