Jacques Thibaud's interpretation should certainly be taken as authentically in the style that Franck would have expected, he was a good friend of and, perhaps, a student of Eugène Ysaÿe, who the sonata is dedicated to. Both of them among the greatest violinists ever recorded.
Alfred Cortot. as well, had a direct musical descent from Franck through his teacher, Louis Diémer, for whom Franck composed his Symphonic Variations. So his style, as well, is probably close to what Franck would have done himself.
Thibaud died in a plain crash ( along with his Stradivarius violin, perhaps the one he's playing in this recording ) in 1953, Cortot had a different kind of crash, he was a supporter of the Vichy puppet government and performed at Nazi events and participated in an advisory council, though his wife was Jewish as were other members of his extended family. No one has ever explained why he did what he did during those years.
Later in life he became quite erratic, despite continuing to perform, some of his recordings strike me as intensely neurotic and painfully tortured, though not as nutty as some of what Glenn Gould did. As I recall, my piano teacher told of seeing him being extremely strange in the post-war years, though he's not around anymore for me to confirm my memory of his stories. One involved a cloak that belonged to Chopin which he would wear though it was never washed. Another of his teachers had studied with Chopin.
I've always had a hard time listening to Cortot's recordings, perhaps knowing his wartime history. This is probably the best performance from him that I've heard.
This late 19th century French style feels like the end of summer to me.