Yeah. Would be best to re-cable that after a deep clean.
While I'm not totally familiar with this Huret gear set I can guess a lot from working on similar period Simplex stuff. Was a massive learning curve for me. The other gear cable is hidden inside the larger barrel in the left hand rear derailleur shifter. These are fiddly and borderline frustrating to work on. The French didn't bother with ferrules, instead they removed a portion of the outer plastic so that is normal for the rear derailleur.
It's imperative to organise your work with lots of containers, degreasing agents, metric open ended spanners, long nose pliers, and impossible to find ultra thin blade screwdrivers. Ideally you need the exploded diagrams too. It good to take photos as you go.
This front derailleur is the same period, but you have the cable pull version which will be a bit more complex:
https://www.retrobike.co.uk/threads/early-50s-la-gazelle-eau-de-nil--the-merlot-aftermath-.450638/post-3314973
The rear derailleur will be a fiddle - I would recommend only removing the pulley wheels for a service.
Your first task will be to break the chain really.