After Verdun, OTL Middle Francia did not survive by the combination of further division between Lothair's heirs and expansion from East Francia.
Let's assume a different Middle Francia ruled from Milan (maybe by Bernard of Italy, instead of the Lothairs) with a strong core in Northern Italy + Burgundy which is not divided by his heirs anymore (Bernard adopts Lombard customs in the heritage over the Frankish ones).
The geographical and cultural situation of such entity (many axis of expansion/influcence: W Septimania-Catalonia, E Carinthia, S Rome and Minor Lombardy, N Middle-Francia, Alamannia) would be good enough for future success under capable monarchs, isolating West Francia to the Ile-the-France and East Francia to Bavaria.
Let's assume a different Middle Francia ruled from Milan (maybe by Bernard of Italy, instead of the Lothairs) with a strong core in Northern Italy + Burgundy which is not divided by his heirs anymore (Bernard adopts Lombard customs in the heritage over the Frankish ones).
The geographical and cultural situation of such entity (many axis of expansion/influcence: W Septimania-Catalonia, E Carinthia, S Rome and Minor Lombardy, N Middle-Francia, Alamannia) would be good enough for future success under capable monarchs, isolating West Francia to the Ile-the-France and East Francia to Bavaria.