Ok. So yes, I would say it's "normal" or at least, nothing you can do and not a console issue anyway.
I guess it's something I'm used to and don't pay attention anymore (I played on One X at release and it wasn't just a little stutter, but a freeze for secondes^^). More likely because the game use every bit of ressources to keep a rather stable framerate and the "additional" ressources required to create the save cause a little stutter while driving fast.