I've just been footling around trying to find something and found this instead - a site which seems to have collected together IGI records for Paris ... beginning with births and baptisms in the Chapel of the British Embassy (in alphabetical order) from 1816 to 1828 and from 1836 to 1839, then marriages there from 1816 to 1845.

https://www.francegenweb.org/dept/listed.php?dept=75