Well it's only proper that the driver is on the left side.
I'm sure you mean "right side" since that's where the Helm station is and where it driver's seat is on European cars.
Anyway, I don't think there's any "in-universe" explanation and there may not even be a decent "out-of-universe" explanation either. The closest I can think of is that it was different from TOS which is what they were going for in TNG's early season? To be as un-TOS as possible?
It's meaningless anyway, the idea is that the consoles on the ship are interchangeable, if Picard wanted his helmsman to stand in the horseshoe railing and the weapons officer at one of the aft stations he could have it set it up that way.