WI: Clovis I converts to Arianism

Anyone of the Byzanophile forumites around here able to take a stab at what 6'th century ERE would do if a strong continuous country, popped out just outside their sphere of interest (Italy is to close to the traditional hearthland and Hispania is to rich not to be interested in, Gaul in itself doesn't really have a compelling reason to control other than to stop attacks from that front) following a branch of Christianity that they've previously stamped heretic? ... would they soften up their reactions, looking at it not unalike the difference between Oriental churches and Constantinople, itself prehaps even in length suggest that the patriarchate is expanded to 6 or would they stand strong on that they are heretics?
 
If the Franks aren't Catholic, I think the Amoricans would be the only Catholic group in Gaul. Perhaps, the Burgundians might be the first Germanics to convert to Catholocism, since they are located close to Italy and have a large population of Catholics in their country.
 
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Anyone of those around here on the forums willing to take a guess what a Byzantine Empire (and the Christian Churches) would do if a strong independent France raised which followed a Christian branch, previously branded heretic? ... as mentioned its probably just enough out of their sphere of interest that i doubt it would be a religious prestige project to kick them down taking over their lands
 
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