Is there a phonological explanation of why the letter “s” dropped in many French words (resulting in adding the circumflex accent)?

Between them, Christopher Ray Miller’s answer and Brian Collins’ answer have most of it covered. There’s one more way to look at it though.

French dropped /s/ at the start of consonant clusters, at the start and in the middle of words. So /sp/ > /p/, /sn/ > /n/, /st/ > /t/ etc: hospital > hôpital, Rhodanus > *Rhodne > *Rhosne > Rhône, establir > établir.

The motivation for this in phonotactics is to reduce the complexity of syllable structures, which make syllables easier to pronounce. It is linguistically common for /s/ to drop off at the start of clusters like that. Dennis Rhodes’ answer notices a similar process going on in some dialects of Spanish (Cuba, Puerto Rico): español ends up pronounced as etpañol, which is on the way to epañol. In my favourite language, Tsakonian, /s/ followed by a consonant is replaced by the aspirated consonant: stoma > tʰuma, sporos > pʰore.