How does one find out whether a particular Intercités train on a particular route requires a reservation?
On SNCF website for Intercités trains, one can find a map of all Intercités de Jour with different line style for those with required reservations.
Giving a quick look at it, this does not seem to follow a specific logic, some lines having both, some lines having only either with or without reservation. There is no geographical logic either.
You can look up the timetables on the Intercités website. Intercité trains with compulsory reservation are marked with a R in a box above the train number. In addition, all Intercité de nuit (night trains) and TGV (high-speed trains) require a reservation, and TER (regional trains) never do.
For the most part, trains with the same endpoints have the same status (e.g. no Paris–Nevers train requires a reservation, whereas all Paris–Clermont-Ferrand trains require a reservation even if you get off at Nevers). Beware that there are occasional exceptions.