Looking up French warship 9104 I see her described by Wiki:
Tonnerre (L9014; lit. Thunder) is an amphibious assault helicopter carrier of the Marine Nationale.
Undoubtedly a very capable ship, but not the first type that springs to mind when selecting a vessel of opportunity for what amounts to hydrographic survey work.
I wonder if perhaps they are using her as a base for naval ASW helicopters to cover a large area with numerous dips of their dunking hydrophones to listen for the pinger(s). Half a dozen of those helicopters could join up a lot of dots and do vastly more acoustic searching in a limited time than a full spec hydrographic survey vessel could ever hope to achieve.
As AT1 points out, the limited track info that we have/had from AIS is not at all consistent with towing a hydrophone eel array, nor with towing a towfish. Hence my speculative conjecture, in which I should have used the word 'surmise' instead of 'conclude', that they were doing some kind of contact investigation rather than the boustrophedontical pattern of an area search.