Their traits, UU and UB favour medeival to early rennaisance warfare. They are, essentially, uber militaristic so if you're not waging war and expanding hugely you're not going to make the best of their traits and UB.
It's worth noting that the AI usually does well as charlemagne in the games I play. (If I encounter him early I make a point of hammering his economy first chance I get).
As it is, Given their starting techs, I'd research archery first while builiding a worker (delaying the worker if it takes a liitle while to develop eco techs by building an archer), then four eco techs (agriculture, mining, animal husbandry, wheel) before beelining priesthood and writing to get CoL.
For five reasons:
1) eco starting techs are poor, while going for oracle to CoL will be quicker than AI will go for it. Besides, your ub should make acquiring an early religion yourself less important. (the reason for acquiring CoL early is the Ub, not confuciansim: that's just a pleasant bonus and means you can opt for other teams religion should you choose. Monastries are cheap and boost research).
2) city garrisoned archers will provide a strong defensive military early.
3) Those settlers will come even quicker if you have developed land first. Expect at least four cities by 75th turn)
4) It makes a chariot rush a very real possibility. You start with a scout, so explore enough land you have a good chance of finding horses.
5) intelligent use of caste system will pop borders quicker than even a creative leader can manage (three turns) and means you don't have to fret about building monuments in your third and second cities (meaning you can build rathaus 1st). Doing so means you lose less money due to maintenance at a time when your economy is less capable of supporting it large empires.
