Approximately,and given the similarities (and that nowadays there's a barcelona-paris direct trip) , i'll base my response on the AVE, spanish TGV :
During summer, the temperature is set between 18 and 22ºC depending on the temperature outside ( the higher outside, the lower) , counting that a lot of people generate a lot of temperature and that human odour is less noticeable on cold air, and during winter, it's set between 20 and 25ºC. Atleast on the spanish trains tho, there's a display that constantly shows current weather, next stop, current outside temperature, current inside temperature, etc...
but yes, in general, and for the average person, it's cold. it's meant to be cold because it's better to keep people not sweating too much in a closed , plane-sized cabin without showers, for long streaks of time.
that black thing above the door is the data screen: