OAL rebooking only happens on the day (or very close to it) and the circumstances are very constrained. If you wanted to share the specifics then we can perhaps let you know what would work in terms of things like Joint Business. However one thing you can certainly do is cancel the BA booking, get a full refund, and use your Skyteam miles to go La Première.
Any connection below MCT will be picked up in the next few days automatically, and your reservation will be flowed on to what the robots have in mind for you.