"Docket" has several meanings. When it's used in a legal sense, it means either:
(1) the record of filings and proceedings in a court case (the docket in XYZ litigation, a particular case);
(2) a register of such records (the criminal docket, i.e., register of all records in all criminal proceedings in the court whose docket it is);
(3) the case load of a court or judge (i.e. list of cases being tried or scheduled to be tried); and
(4) by extension/analogy, it can also mean an official register of any type of legal records.

It's meaning (4) that you have here: the register of marriage licenses. (In the US you have to apply for a license to get married, and then after the wedding your officiant returns a signed document to the town hall where the license was granted, and that document is filed together with the marriage license to show that the marriage occurred.)

Best FR translation: registre des mariages. Example (random, from the Strasbourg archives): https://archives.strasbourg.eu/archive/recherche/etatcivil/n...
That page lets you search, by checking a box on the left, the "registre des mariages," among other registers/dockets.