That makes absolutely no sense.
HYDRA used the payments to Batroc as part of their attempt to hide the real reason Fury was assassinated, yes. But the Lumerian Star was a HYDRA asset, disguised as a SHIELD boat and launching the Insight targeting satellites. The only reason HYDRA attempted to assassinate Fury, thus necessitating the cover up you're talking about, is that he caught wind that something was suspect in the Insight program. You don't aim Fury at the Lumerian Star if you want to frame him, because that's where you are doing nefarious deeds. If Fury had no idea what was going on, why would HYDRA launch a plan to frame Fury that required them to first put him on their trail? Or that might expose their secret plan to additional scrutiny in the final stages? Why not just, you know, keep their program hidden and let it launch as normal?
Fury was already suspicious that SHIELD had been compromised. He used Batroc as a decoy so that he could have Widow access the Lumerian Star computer, which led him to files that told him he himself had encrypted them, even though he knew he hadn't, which confirmed his theory. He goes to Pierce to try and stop the Insight launch, inadvertently revealing to Pierce that he was on to part of HYDRA's plan and resulting in his meeting with the Winter Soldier. Pierce simply made use of Fury's trail in an attempt to hide the fact that HYDRA "murdered" Nick to cover up their nefarious plans with Insight.
The entire film is a back and forth between Fury and Pierce over who is actually a step ahead the entire time. Fury doesn't realize who he's playing poker against at first, but the whole thing is basically Fury drawing into HYDRA's otherwise winning hand. Pierce develops Insight. Fury figures out something is rotten in Insight and makes his play with Batroc. Pierce responds by raising the stakes with his super soldier. So Fury calls by putting his own on the table.
But it's true, in terms of Batroc, it doesn't actually matter. He goes where the money is and doesn't care. It's only relevant because it's Sharon hiring him, and our choices are "she's up to shady and nefarious things because she's evil", or "he's the go to patsy when you need a merc to open a door you can't be seen to walk through."