Many of the trains on that route are Intercites, and the fares do vary, typically increasing as your travel date approaches. I took a quick look, and it appears that one-way 2nd-class fares can be as low as 9 euros or as high as 20 euros. It's possible that fares could even go outside that range.
I'm not sure what the deal is with reservations on the Intercites trains to Vernon; apparently Intercites trains usually require a reservation, but not always. If your potential trains require a reservation, you could run into a sold-out situation if you wait until the last minute to buy. In looking at prices I found a train that had only 1st-class seats available, which I assume means all the 2nd-class seats have been sold.
There are some TER (regional) trains as well, and you can always get on one of those (standing if necessary). However, if a strike causes cancellation of a lot of trains, squeezing onto a TER could make for a rather unpleasant ride. Also, the (fixed) fare on the TERs is a bit higher than the lowest prices on the slightly-faster Intercites trains.