Theatre, I will give you, but not centre (though "theater" is still the dominant spelling in America). The spelling "Centre" is extremely rare in the United States. For example, there's Centre Street here in NYC, Centre County in Pennsylvania, and Centre College in Kentucky. However, those places got their names before there was standardized spelling in the United States.
Just looking at Google Trends will show you that "Center" is clearly king over "Centre" in the United States (https://trends.google.com/trends/explore?date=all&geo=US&q=centre,center). Americans would almost never write or type "centre" unless it was a mistake or they were trying to be British, Canadian, Australian, and so on.
The "-our" word spellings are unnecessary. The extra u is not needed. Most of the "-or" word spellings are how those words were originally written in Latin. In Spanish, "color" is "color" and in Italian "color" is spelled "colore". The French added the unnecessary u (and this spread to the British through the Norman invasion, who in turn spread the "-our" when they colonized the world). If you're going to bring the French into this, what about some of the pronunciations? What about "fillet"?
Theatre is still prevalent overall. The Oscars have been presented at either the Kodak Theatre or the Dolby Theatre. We also have large theatre companies such as AMC Theatres. Centre is less common than theatre, but I've seen it in many places. It's usually around plazas or shopping centres. If we pull in the Constitution, we should using -our and -ce spellings. The Constitution uses "behaviour" and "offence" and "defence".
As far as what's needed, English will look quite different if that's all that mattered.
^This.
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