I've seen the term "trail running" translated as "course à pied" and "course de sentir". I appreciate one may be grammatically correct and the other a colloquialism, or something similar.
As far as I can tell "course à pied" transliterates as "race of feet" whereas "course de sentir" is "race of feel(ing)".
Are both terms correct or interchangeable?
"Course à pied" is just a generic term for running, even though the literal translation might seem a bit funny.
I have never heard the term "course de sentir", which doesn't really mean anything, but I think what you meant instead is "course de sentier", which would be a literal translation of trail running, a trail (in the woods) being a sentier (dans la forêt).
The French Wikipedia page refers to it as "trail", "course nature" ou plus rarement "course en sentier".
You are mistranslating course à pied.
"Race of feet" would be course de pieds which is equally non-sensical in French.
À pied litteraly means by feet, i.e. using our own feet as "transportation method", just like we say à vélo, à cheval, or en voiture.
We say course cycliste, hippique, automobile for the former, and we might say course pédestre for course à pied, but the latter is much more common.
Course de sentier is not idiomatic.
Course en sentier : « Course à pied se pratiquant sur des sentiers balisés. » (GDT)
Course de pleine nature : « Course d'endurance en terrain naturel et varié, dans laquelle les concurrents enchaînent des difficultés pouvant imposer une alternance de marche et de course. » (Franceterme ; GDT)
