As a French person, I’d say it is a specific case: the root “comp-” is never pronounced with a “m”. For instance, the “m” is silent in “comparable”, “compatibilité”, etc. It is also silent in “comte”.

However if there is a double “m”, then it is pronounced: “commutation”, “commère”, “commentaire”.

Compte is pronounced the same way than conte and comte.

The problem for you is the “-omp-” part: in this case it’s pronounced like a “on”.

The same sound than in bon, maison, garçon, leçon…

The classical grammar rule says :

“before m, b, p, one always replaces the n by an m. The only exception is the word ‘bonbon'”

The French prefix “con” is also used in English, and means “with”. Without that rule, we would write “conmerce”,”conbinaison”, “conptable”, but the rule being applied, we write “commerce”,”combinaison”,”comptable”,