All those culture groups in the West at the time were Germanic, and Charlemagne had united France, and created the Holy Roman Empire, and conquered some remnants of Italy. After the death of Louis the Pious, these lands were divided by his sons in the Treaty of Verdun, so it was very easy for foreigners to still have no distinction between them long after Charlemagne's death, because they were the same Frankish rulers, but the rule did not last very long... By 888, the Carolingian Empire was on the verge of destruction, under constant attack from Vikings, and the now distinct seperation between their Germanic Eastern Francia, and Western Francia Kingdoms was more noticeable. Note that East Francia is an archaic term for the Kingdom of Germany, thus not helping to establish a difference between cultures. This being said, the educated of Byzantium most definitely knew the difference between the cultures during this time, and those who didn't, surely knew by 1000AD, as East Francia generally ceased to be a term after its fall from Frankish holding, in 962. However, the establishment of the Franks as a premier European power at these times generally leads to people just calling the entire area as they see it; a land filled with Franks, but as I said, the educated of these societies surely knew the difference of lands and specific cultures. Kind of the like modern term 'America'; when you say it we all know what you mean, but realistically, the term America can cover both continents.

Piggy back question, did European Crusaders consider all Muslims and Middle Easters the same or did differentiate between Turks and Arabs.

Quick question about my purely speculative assumption: Does the term "lingua franca" not come from the fact that French was the language of the western European ruling class for a very long time?