I already asked about the use of circumflex accents to mark the former presence of a deleted letter here: Circumflex and deletion of letters.
The word "théâtre" in French requires the circumflex accent on the "a", and this is the only currently accepted spelling, afaik.
After a bit of research, I could not find any conclusive indication as to why the "a" comes with the accent in French, more so if one considers the etymology "theatrum" in Latin and "θέατρον" ("theatron") in Ancient Greek, which do not seem to carry any "extraneous" letters.
Is there a plausible explanation for the presence of the circumflex in "théâtre"?