Is there a connection between the existence of Medieval Blue Men or Black Men in Europe and Blue Blood meaning the Nobility?

In a Word, no. Blue blood comes from the bluish coloured blood which many of the nobility attained from silver poisoning via their cutlery. Since this was not understood, and the poorer members of society could not afford silver cutlery, blue blood was said to be a sign of noble heritage.

In Old Norse, blamann translates literally as blue man, but bla could also mean dark, or black. The Norse used blamann to describe the North Africans which they encountered, and when they came to Scotland and Northern England (which had languages which were mutually intelligible with Old Norse), the term stuck.

To Elaborate:

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