About the “possibility” of Cherokee in your bloodline: if your family hails from the Southern US, that’s a Southernism. Many White families in the South claim to have Cherokee blood; it goes back to some concept of claiming “ownership” of the land that actually belonged to the Cherokees. However, almost none of these claims can be substantiated. An example of someone who’s gotten burned by this is Elizabeth Warren, whose Southern family has a “tradition” of Cherokee blood; she’s 100% White. Pretty much any White person claiming to be part Cherokee isn’t.
If, however, your family hails from, or originally lived in, the upper parts of New England, and your makeup is partially French (which you don’t indicate), then the possibility of a tiny amount of Native American blood (much less than Ms. Warren claimed to have, I might add) exists, because the French really did intermarry with the Native Americans in Quebec and the surrounding areas. It’s not enough to mention, unless you’re documenting your ancestry.
It’s unfortunately just one more thing to NOT be proud of, about being White. :-/