WI:Bohemia is annexed to the Frankish Empire in the Carolingian times

Good question. My guess is "not much", the social structure and general development are too dissimilar to the core Carolingian territories and too far from them to be effectively assimilated before it goes down the drain. But a Christianised and nominally imperial Bohemia could have very interesting effects down the road. It might even get us written copies of Western Slavic mythology and folklore surviving to this day.
 
Looking at Slovenia should provide you with an anwser, because what you are asking is the history of Slovenia just at a bigger scale.
 
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