Gents,
It's a bit confusing, and the OP's own confusion doesn't help, but the "treaty" in question dealt with payments for seizures made by Revolutionary French privateers before, during, and after the Quasi War period.
If memory serves, the US and France negotiated an understanding around 1801 in which France agreed not to seize US merchant ships. That understanding offered compromises on several levels. Both parties agreed to a specific date in 1800, sometime in August or September comes to mind, before which France wasn't liable for any seizures and after which France would be liable for any seizures.
For various reasons, things moved slowly after that. The 1803 Louisiana Purchase treaty restated the original agreement and 30 years later the parties finally agreed on just what the term "liable" would mean France was liable for. France agreed to a lump sum payment regarding the post-1800 seizures. France would hand over the money and it would then be up to the US to identify, investigate, and, if justified, pay off the various "spoliation" claimants.
Once again, more important domestic issues arose, i.e. all the shenanigans surrounding the July Monarchy, and France put the matter on the back burner. For it's own domestic reasons, the US kept pressing for the money, even though the ship seizures were a generation in the past. France got fed up with the whining, told the US no money would be forthcoming, and Jackson got his back up.
Again, IIRC, the whole matter was resolved soon afterward for pretty much the original amount agreed upon.
Bill