I think you might have nailed it !
I am rather new to the X-Plane world and still fiddling with things. I'm using SkymaxxPro, RealWXConnector and XPNOAA weather and I think I forgot to check the wind on that specific test where I had the issue. And as an added factor, I am more used to the 737NG/747/777 screen layout and so I might not have paid attention to it on the ND.
I just ran another quick and dirty test with almost no wind this time, and did not see the issue !
But once on the runway, the aircraft did not properly track centerline. But I did notice that there was no "rollout" mode on the FMA.
Sorry to bother you again (promise, I'll start working on my FCOM !) but on the 737 classic, when performing an autoland, are you supposed to disengage the AP as soon as you are or the ground ? On the 747 for example, where only ailerons and elevators are controlled by AP in normal modes, when going to LAND3, rudder becomes active too, and on the runway, aircraft does follow the centerline. But once again it is not the same aircraft so this might be a 737 classic specificity.
Many thanks for your very kind support.
Charles