When a Data Courier wakes up in a French hospital with no idea how he got there, he must finish his delivery that may prevent or start a war, only he can’t remember whose side he’s on.

That sounds very much like Johnny Mmemonic, the film with Keanu Reeves based on a William Gibson story.
Here is my attempt:
In the near future, when a data courier storing messages in a cybernetic cranial implant suffers a car accident erasing part of his personality he must evade deadly pursuants sent by two factions at war whilst trying to piece together which side he belonged to.

From reading the logline (not considering other loglines you posted prior) it isn't made clear that the data transportation device is his head - most first time readers of your logline would assume you're referring to a HDD or memory stick of sorts. Making him the actual data storage device is cool but at the same time complicated.

If you want to keep the brain as storage device gimmick, it seems you have two options.
On the one hand, seeing as him carrying data and subsequently requiring a "brain format" after each delivery is crucial for the logic of the story, it might need to be mentioned in the logline. On the other, brain = HDD adds a large amount of information for one logline to hold and therefore may need to be omitted from the logline altogether.

If the former, you run the risk of detailing too much and losing the producer's attention. If the later, you run the risk of creating confusion with the logic flaws in the concept.

Normally when a plot requires extensive explanations to be made immediately clear, it's indicative of a fundamental problem with the story. I'm not sure whether or not that's the case here, but it's worth considering an alternative at this early stage of development.

What is this story really about? Is it about the cool brain = HDD gimmick? Or is it about a soldier struggling with the dilemma of who he can and who he can't trust to save the world?

Pending the above question, I think you could rewrite the logline with more clarity.

Knight, the explanation of his condition is for the movie itself. The logline is an encapsulation of the setup, the main character, his struggle, goal, and if possible, how urgent achieving the goal is before the resulting situation.