It’s usually cheaper to book in advance. In particular if you want cheap seats on the Eurostar you have to books months in advance.
The Interrail reservations/supplements are fixed price (or for some SNCF trains there are two price levels as the train fills up). But their number is limited, so in a way the advice is the same.
Eurostar Snap used to be cheap as balls. 19 quid. Though going there it seems that it's no longer available https://snap.eurostar.com/uk-en
What a pity. Lots of fun weekends in Paris on that when I was younger.