How far in advance to book train tickets in France

You will get the best fares if you buy them in advance. Discount fares come out about 3 months (?) ahead but they are limited. Once they are gone you are left with the higher price fares. If your dates are set then it makes it easier to buy the tickets. There is not much difference between 1st and 2nd class and they both get to the destination at the same time. Check out www.seat61.com for more details about the train.

Tickets are for sale now and the cheaper rates you see have limited seats available. Prices will only go up as those sell out. The advance booking locks you into a date and time for each trip.

You also would be a candidate for a Eurail France Pass, for instance the current price for 5 travel days within a month is $201 per adult in 2nd class or $268 in 1st. TGV trains require separate seat reservations of about $11-27, but they no longer have artificial limits for passholders on domestic routes. You can make some of those at the same time that you buy the pass, or book on shorter notice in stations, but note that it's possible for trains to sell out, especially around weekdays, holidays, and special events.

Don't buy any pass without pricing the point-to-point tickets first to see if the pass is worthwhile. Remember that many French inter-city trains (not all) require a seat reservation that must be bought separate from the pass.
One repeated knock against Eurail is that its selections may not be complete.

While the 90-day advance is the common limit, SNCF, the operator, sometimes puts on sales further ahead than that. On its site you can sign up for notification.

https://en.voyages-sncf.com/en/

Between Lyon and Beaune it is a TER train. No advantage to advance purchase as price is always the same and they do not sell out.
1st class is not necessary in my experience. And on TGV's, you will not be on the train very long.

Essentially you're trading convenience/flexibility for price. You can save quite a bit by booking well in advance but it locks you into an itinerary. If you later decide to change your schedule, it will cost you both some, or all, of the value of the ticket you already purchased plus the cost of a new ticket.

Passes are rarely a good idea in France for long haul trains (they are great for the metro but that is a different kind of pass). The cheapest tickets get snapped up shortly after tickets go on sale. Tickets go on sale at least 90 days out and for summer season sometimes earlier. The price is about a third what you pay last minute and often less than the cost of the reservation when you have a train pass.

There is not much difference between 1st and 2nd class and they both get to the destination at the same time.

The latter part made me laugh. And I agree wholeheartedly.

Slight tangent question...
What about short distance trains like Marseille-Cassis? Should those be booked in advance?

There's no advantage to buying Marseille-Cassis tickets early. It's a 23-minute ride on a TER (regional train), and those ticket prices do not change. Just be sure you allow time to buy the tickets before boarding. I have very little experience buying outbound rail tickets in Marseille, but I did run into some delays in Nice when there were multiple people lined up to use each vending machine.

Tickets are already on sale for these dates. The longer you wait to purchase them, the more expensive they'll be. Of course you'll need to have decided on your itinerary before purchasing, and you're locked into the specific trains that you buy tickets for.