Type bias in either direction doesn't really have a place in any analysis. If she's S, she's S; and if she's N, she's N.
I could do more extensive research, I suppose, except that the issue is not important enough to me to invest the time right now. Another problem is that there have been enough docu-dramas, movies, whatever else, rather than pure historical record, so without more research I cannot say for sure which presentation of Joan I'm responding to.
But in the past, my impression was that her major qualities seemed to me to align with INFJ style behavior: Internal vision of what's "true" even when she faced severe opposition in the external world (to the point of death), an external Judging function, and her focus was long typical Idealist lines. She didn't uphold status quo, she just did what was right. There's an unwavering fierceness to it that is typical of IxFJs.
SP behavior is more concerned about freedom and flexibility, although they can also be moralistic. But we're really taking about the "grounding reality" here, and Joan's inherent world view was a moralistic one built on a spiritual connection with the Divine that she saw as inherently true -- this is typical of Ni just "seeing the dots connected" without having to process anything even if no one else does. It wouldn't surprise me if she could argue with church leaders and point out flaws in church theology and practice, either; look at some of the more involved INFJ's here and see how functional their Ti is, in service of their values. Ti is the "hole finder" in the underlying structure of things.