I've been doing a bit of work on this. And I started just where you'd expect me to start - at the end.

I've written some code for Baldewyn Coffier to take over the store, except that he doesn't really - as previously suggested, character "Arnaud Matton" becomes a clone of Baldewyn Coffier so that everything in the game system which expects "Arnaud Matton" to be there will still work. Actual character "Baldewyn Coffier" disappears, while the original street merchant displaced by Baldewyn Coffier returns. There's some checking on Sabine Matton's "quest.hire" attribute. Mostly it will simply change to "done", which means if you haven't already done anything with her then you've missed your chance, and if it was previously "enemy_forever" so that Arnaud would refuse to trade with you because you demanded a ransom, the Baldewyn clone won't hold the same grudge. If it's one of the values which indicates that Sabine is your prisoner and you're on your way to collect a ransom, Sabine changes to an actual prisoner in your hold with normal prisoner dialog so you can ransom, release or recruit her as with any other prisoner - you won't get any ransom from the Baldewyn clone! But if you had previously told Arnaud that you were taking Sabine to Sylvie Bondies and have not yet done so, you can still take her there and either hand her over as you promised, keep her, or demand ransom from Sylvie Bondies and then either hand her over or keep her anyway - and choosing to keep Sabine again makes her a prisoner in your hold, to be ransomed, released or recruited.
I've also done a bit of work on "Joseph Claude Le Moigne_dialog.c". Once Baldewyn has finished taking over the street trader stall and paid back your loan, you can talk to the governor about how Arnaud Matton swindled Baldewyn Coffier out of the store. If you have no evidence to back up this accusation (which you don't, because there's currently no way to get it), the governor warns you never to repeat it - and if you do repeat it to the governor, he calls for guards. Overriding that, if you're hostile to France (or Spain in "Early Explorers"), the governor calls for guards right away. Overriding that, if you've demanded ransom for Sabine, the governor says that Arnaud has accused you of kidnapping her and calls for guards. Overriding that, if you're at least rank 7 with France (or Spain) and have reputation at least Dashing, the governor recognises your record of distinguished service, takes your word for it, promises to investigate, and Baldewyn gets the store back after about a month. Or, if you've captured the town for yourself, the governor is your former officer, still regards you as his captain, and puts Baldewyn into the store immediately.
So there are a couple of potential shortcuts to completing Baldewyn Coffier's quest, but for the most part, you'll need proof before you go to the governor...