Yup, in French that circumflex is kind of etymological. I say "kind of" because that /s/ being dropped changed the pronunciation of the preceding vowel, and depending on the vowel and the modern dialect there might be some leftover of that change; for example ⟨tâche⟩ /tɑʃ/ "task" vs. ⟨tache⟩ /taʃ/ "stain".

Originally the diacritic backtracks all the way into Ancient Greek. Back then Greek had a pitch accent, and a vowel could either raise in pitch (so it got an acute, ά) or fall (so it got a grave, ὰ). But some long vowels and diphthongs did both things, raising then fall, so the solution was to mark it with both, as ᾶ. Eventually that circumflex evolved into a tilde-like shape, but that's a coincidence.

Other languages might use it for vowel length, vowel quality, stress.