“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)