Define "different sort"? Someone else is going to ask you when in the 11th century but I'm going to go in a different direction, because I don't believe that the mutual excommunications of 1054 were widely recognized at the time. Their significance grew with distance. The Latin excommunicators didn't even believe that their excommunication would hold, because when they did it they knew that the Pope who sent them had just died.

The other question is which French Christian? Most French Christians wouldn't have known enough to have an opinion on the subject until people started returning from the First Crusade in the last few years of the 11th century. During the first 90 or so years of the century relatively few people in France would have known much about Byzantine Christians beyond knowing they existed. During the last ten years of the century whatever differences that existed would have been papered over as the Church preached Crusade to assist their Christian brothers.

It's likely that some priests or monks would have had opinions on these subjects. I think a learned Latin Christian priest or monk from France would have recognized that the Byzantine Christians were culturally different and practiced their faith differently, and even that there were theological and practical disagreements between Latin Christians and Byzantine Christians. I doubt anyone would have seen a bright line until people started returning from the first crusade and complaining about how weird Byzantine and Middle Eastern Christians were.