If you think they're the person in overall charge of payments and receipts, which they probably are, you could call them "chief". Otherwise just cashier.
http://www.dictionary.com/browse/cashier

Even if there is an exact equivalent of this position in US or UK municipal governments, it won't have the same title everywhere. Cities ten miles apart might use slightly different names for it. So this is a situation where you need an explanatory translation, so that the reader understands what (or in this case who) you're talking about.

The French definition says it's a human being (not a business entity) whose task is to handle what we call in English either "accounts payable" or "accounts receivable," for a municipality. The context of the term in the OP's text will tell OP whether it's accounts receivable (money owed to the city) or accounts payable (money owed by the city).

Accounts payable and receivable departments are subdivisions of city finance departments (link: http://www.munitemps.com/2018/06/14/accounts-payable-whose-j... That corresponds perfectly with the "régisseur" definition stating that the régisseur works "pour le compte du comptable public."

As for the final word, my first thought was to say "accounts payable/receivable clerk," but clerk is usually a low-level position. "Administrator" also makes clear (like clerk) that we're talking about a human being rather than a business entity (which is also part of the definition of régisseur). The advantage of "Administrator" is that it's not clear whether it's high level or not. It could be: an XYZ Administrator could be the head of the XYZ department. So I would prefer Administrator to Clerk, to allow for the possibility that the Régisseur is the highest position in his or her department.

Hello
I have a Proz entry to back this idea albeit the context is different but whenever you see "régisseur" on a government form and with a signature, this is a good bet.