There are now a couple tools to compare the prices of train/bus/rideshares. Two examples are Comparabus and kelbillet.
Trying these for a trip in October, 3 months ahead of time, the bus costs from 35 to 50 euros to Bayonne/Hendaye (in my experience, for such distances the price does not vary too much, even a week in advance), the rideshares are available later (booking 1 week in advance is enough, and there are often trips available one day before) and cost around 60 euros (rideshare prices are quite stable) and the train starts at 50 euros (and there are direct night trains between Paris and Hendaye, but they may disappear in 2017).
Overall, if booking early, you might find trips for as low as 35 euros, and in general you can find reasonably priced trips at 50-60 euros, even a day before. Rideshares are getting very popular with the blablacar website in France.
One more thing, France transport network is really centered around Paris. Searching for Lille-Paris and Paris-Hendaye is likely to show cheaper options than Lille-Hendaye (typically, the train between Lille and Paris is one of the most expensive segment in France - while I paid <10 euros last minute in a ride share -, Paris-Hendaye is more competitive - I paid 30 euros by bus, 60 by train a week or two in advance)