Carnac seems to be a Gallo-Roman form.
"The Fairy-Faith in Celtic Countries"
W. Y. Evans Wentz
The withdrawal of San Gallo, and the deaths of Giacondo and Raphael in 1515, led to Baldasarre Peruzzi being appointed architect, and under his auspices the plan was changed to that of a Greek cross.
"Architecture"
Nancy R E Meugens Bell
Both were probably the result of continental influence; but, while the church at Hexham may have been the work of Gallo-Roman masons in direct communication with the general current of architectural progress, the church at Barton was probably built by Englishmen, who adapted the centralised plan to methods natural to their comparative want of skill.
"The Ground Plan of the English Parish Church"
A. Hamilton Thompson