Yes. Here's the save, you just need to dock in Marigot. After talking with Suzanne, the store will be closed. Perhaps you missed something when transferring the quest to free play.
Here is the last case that worked.
Quest name fourth_mission_to_jean FOUND in SideQuestComplete
I tried that save and immediately ran into trouble. The fort fired at me. The reason is often shown in "compile.log", as it was this time - the fort remembered me as British. You must have been somewhere near Saint Martin flying a British flag and forts can see a long way. So when I ran away from Marigot, went to worldmap, sailed clear of the island, raised a British flag and then returned to the island to sail to Philipsburg, the fort there fired at me because it had seen me with a French flag. So you can't land at Marigot or Philipsburg. At least, not until you get a different ship because the forts remember you in that particular type of ship. You have a British Letter of Marque - use it! Capture a French or Spanish ship, keep it and sell your existing ship, then make sure you're always flying a French or Spanish flag when you approach Saint Martin.
However, I have my own play through "Tales of a Sea Hawk" with saves from every time I was about to talk to Beltrop. So I loaded the one where I was about to report completing the first mission, then played the second mission and went to prison, then completed the third mission, then sailed to Philipsburg - I've always approached under a British, Dutch or Portuguese flag, so Marigot will attack me but Philipsburg is safe, and there's a tunnel between Philipsburg and Marigot. Sure enough, the store was closed. I added that line to "second_mission_money_not_delivered_to_beltrop", then did it all again, and this time the store was open.
Also, after I opened the door using the console command, he greets me 2 times. This happened in my last playthrough, but it really catches my eye.
Locations[FindLocation("Marigot_port")].reload.l6.disable = 0;
The first time he says lines 1 and 10, and the second dialogue is 31 and 32 "France Trader_dialog.h". It’s probably better to make sure that there is no standard dialogue, but 31 and 32 at once.
He shouldn't be using line 1, partly because he should be starting with dialog case "second time" which begins with lines 7 and 8 (or with line 9 if you have a bad reputation), but mainly because line 1 is the "DLG_TEXT" declaration! Line 2 is used by dialog case "First time" but he should only use that when you talk to him for the first time. After that, he's set to use "second time" by default, and quest case "fourth_mission_acepted" also sets him to use "second time".
So he starts by greeting you as a customer. That way, if you land at Marigot and need to buy supplies for your ship, you can buy them from him before saying line 15. That leads to the dialog about Beltrop's mission.