John Hawks found a paper analyzing the height of Charlemagne (742-814). Rühli et al. (2010) looked at measurements of Charlemagne's left tibia in order to determine his total height and robustness. The result indicates that he was 1.84 m tall (6' 0"). This is considerably taller than the average height of his male contemporaries at 1.69 m (5' 6"). Thus Charlemagne was taller than 99% of the men around him and qualifies as "great" in more ways than one.
The average height of Germans today is 1.78 m (5' 10") and Belgians are a bit taller at 1.795 (5' 10½"). (Charlemagne comes from the area around Liege in Belgium and Aachen in Germany.) Charlemagne would be taller than average in today's society but not notably taller.
The average height of Europeans (men and women) has increased by about 9-10 cm (3½-4") over 1200 years. This isn't as much as most people believe but it's still significant. (Most people who have visited Medieval Castles take note of the small doorways and assume that contemporary Europeans could pass through them without bending over. Not true—they also had to stoop to get through.)
Is this height increase due to evolution or better nutrition? When presenting this question to my students, I point out that you can only answer the question if you have a good definition of evolution. The definition of evolution I prefer is, "Evolution is a process that results in heritable changes in a population spread over many generations." The key word here is "heritable." In order for average height to be an example of evolution you have to show that the genetic composition of today's European population is different from that of 1200 years ago. In other words, a change in frequency of "tallness" alleles accounts for the change in height.
That's not very likely, so we're not talking about evolution here.
Recall that Charlemagne is almost certainly your ancestor as long as you have some Europeans in your family tree [Are You a Descendant of Charlemagne?]. I happen to know how I'm connected to Charlemagne [My Family and Other Emperors] but he's almost certainly your ancestor even if you don't do genealogy.
Does that mean we all descend from a taller-than-average 9th century European therefore it's no surprise that all Europeans are taller today? No it doesn't mean that at all. Charlemagne is your ancestor—if you are of European descent—but so is everyone else who lived around him. That includes the pig farmer who lived in Herstal, and the midwife in Aix-la-Chapelle. They were average people. Some of them were much shorter than average.
[Hat Tip: John Hawks: Charlemagne the Tall.
Rühli, F.J., Blümich, B., and Henneberg, M. (2010) Charlemagne was very tall, but not robust. Economics & Human Biology 8:289-290. [doi:10.1016/j.ehb.2009.12.005]