But the late Carolingians were mostly centered on Laon (snort)
Laon cannot
ever be the capital of France, in the same way Ravenna cannot ever be the capital of Italy. It is basically a big hill standing in the middle of a huge plain: a refuge fortress, but not good as a capital (out of center and waterways - though it does have a good agricultural hinterland).
The two main contenders for Paris are, in my view,
Lyon - strategic Rhône/Saône confluence, but a bit remote from the center
Orléans - well situated on the Loire with good access to the Beauce, important post-Roman city, right in the center of Gaul, but not an impressive defensive position (the Loire islands are notoriously sandy: impossible to build such a good defensive position as the Île de la Cité). Alternatively, Tours also makes some sense, for access to the Cher river.
But all of these cities are plausible only if Gaul is more southern-focused than France. Which probably means only limited influence from the Frankish invasions. But as long as France is France, its capital is going to be located where the Franks are, i.e. in the center-north part.
Well, if you want something really exotic:
* Visigoths focus north.
* They beat the Franks, the border between them is now roughly at the Seine & Oise rivers.
* Visigoths now control most of Gaul and move their capitol from Bordeaux to Orléans.
* The northern part is now called Kingdom of Francia. Its capitol is Amiens.
There, you have
both capitols at Orléans (for most of OTL France) and Amiens (for this ATL France entity). But this is probably not stable in the medium-long term.