I think he'd at least by sympathetic to the New Deal, after all it was modelled after his Square Deal, but whether he'd vote for FDR would depend on familiar tensions.
There weren't any between Franklin and TR. TR ADORED him and said to him once that if he could have had one wish it's that "you would've been a Republican".
Yeah, the one who hated FDR was TR's daughter, Alice Roosevelt Longworth, who was a fascinating and idiosyncratic woman not all of whose views reflected her father's.
Don’t forget his ultra-right-wing son Archibald.