I've heard it (or read it) that the French monarch only really governed France and his vassals were de facto independent. Were other monarchs similar?
Also, were the mid-and-late Medieval French monarchs weaker than Charlemagne's successors or were they of comparable authority?
All of this is obviously dependent on the exact period, and relative power isn't an absolute thing, but at the time of the Norman Conquest the French king was quite weak compared to his neighbors.
The most obvious example of the weakness of the king in this case is William the Conqueror himself who, despite being a vassal to the French King, was able to defeat Henri I on multiple occasions before he became King of England. Henri was essentially a prisoner in his own demesne and William wasn't his only vassal that was more powerful; the counts and dukes of Champagne, Blois, Chartres, Anjou, Maine, Normandy and Flanders were all individually more powerful than the king.
Once William was King he was able to distribute English land such that he retained a great amount of power over his vassals and over his kingdom in general.
Similarly, the Holy Roman Emperors of the time, Henrys III and IV were both quite powerful, though Henry IV had some struggles consolidating Imperial power (and a civil war, which he won despite losing the major battle). Overall though, they weren't in the same precipitous position that Henri I and Philip I of France were in - they were at least able to meet the challenges head-on.
Overall, the French kings of that period were comparatively weak compared to their neighbors. As for other periods of time in the middle ages, perhaps someone else can chime in.
I'd be interested if someone could also comment on whether or not the relative weakness of the early French monarchy was an influential factor in the development of absolutism later in the 16th century.
If so, can we see an analogue in the the absolutism of the Tsars of Russia whose predecessors struggled with the boyardom?