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Carloman's stats are randomized. If he has particularly poor traits, particularly affecting opinion modifiers then re-roll. For example I'd re-start if he had the Craven trait.

Take War Focus. Spend some time initially stabilising Middle Francia. If you can't manage solid control of half of Francia then things will immediately fall apart when you expand to control the whole of it. Try to create a couple of duchies, since you will soon be overwhelemed with too many vassals. Taking this stabilisation time will also reduce your "short reign" penalty.

With Middle Francia stabilised, duel Charlemagne. Kill him or die trying. This will immediately make you king of the whole of Francia. That's when the difficult part comes. You will now have far too many vassals, the Kinslayer trait and factions popping up at a rapid rate. If you don't deal with the excess vassals you will have no income. So move counts, particularly the most annoying, rebellious counts, under control of nearby Dukes. Reshuffle your council. Arrest plotters. Maybe fight the odd civil war of two. If the "Increase cancel power" faction fires, give in to demands - you want the opinion bonuses this gives you. Also don't be afraid to give a few recalcitrants (temporary) independence in order to break factions. Do whatever it takes to stay on top and eventually things will stabilise.

When you finally have Francia under your iron grip, just sit back and wait for the gold and piety needed to create the Empire. Maybe attack a few pagans for extra piety?