Maxwell Duveau has sent you out to protect his client, Quentin Fresnot. However, you know one person who might be interested in this information -- Josette Mercado. She's sure to pay more for the information than Maxwell Duveau. Track her down and meet with her.
First, speak with Josette Mercado. She'll tell you to stir up some trouble by targeting French shipping.
You'll need to defeat 6 French ships on the Open Sea. (Despite the mission text, these ships can be fought anywhere; you do not need to be near St. Rose's Bay. There are also no level limits, so feel free to target any French ships that you're comfortable defeating.) Remember that this will cause your standing to decrease with whichever French faction you target.
Next, return to St. Rose's Bay. You'll need to speak with the Town Boss, Samuel Duveau, followed by speaking with Maxwell Duveau again. Finally, return to Josette Mercado and tell her everything is in place.
The next portion of the mission is a sea battle. You'll start with two allies, Josette and Dylan Fryer. If Josette is defeated, the mission will fail.
Once you've spoken to Josette, your first target will appear, along with two escort ships. The target will flee rather than fight; while there's no escape point for him to reach, if you kill his escorts first you may have a long chase before you can catch up and board him.
After boarding the target, Maxwell Duveau will spawn in, along with three escorts, near your initial spawn point. Once you speak with him, the main portion of the battle begins. You'll be faced with three groups of enemies: Maxwell's three escorts(although Maxwell himself will remain friendly and not participate in the fight), a group of three French attack ships, and a group of five additional French attack ships which spawn in tandem with five allies, including the town boss.
Thankfully, you don't actually have to win this fight. All you have to do is reach and speak to the town boss, then return to and speak with Maxwell, without any of your named allies dying. Once you've done this, you'll enter a new instance where you confront Maxwell with your allies and your faked evidence. After some back-and-forth dialogue, Maxwell will turn hostile and summon some reinforcements. Defeat them in avatar combat (without Josette or the town boss dying) to complete the mission.