The doublets gentle and genteel illustrate the way words from the same Latin original can change in meaning in the course of centuries.
Both words come from Latin gens, “race” or “clan” by way of one of its forms, gentilis, meaning “of the same family or clan.”
In Roman culture nothing was more important than one’s tribal origins. Family names like Julius and Cornelius indicated the clan (gens) to which one belonged.
Gentle came into English from Old French gentil, “high-born, noble.” It was an adjective indicating social status. A person of “gentle birth” was one who’d been born into the privileged classes. This original meaning is still present, at least for some speakers, in the word gentleman. A “gentleman” behaves in a certain way. He is courteous in speech and in behavior. He protects the weak and is kind and generous in his dealings with people of lesser status. He is educated.
Over time, gentle came to refer to a way of behaving in a mild, non-violent manner. By extension, the adjective can be applied to non-human entities: a gentle hint, gentle punishment, a gentle horse, a gentle voice.
Genteel came into English as a second borrowing from French, this time with the meaning of “nice, graceful, pleasing.” In modern usage genteel has a negative connotation. An excellent example of someone to whom the word applies is Hyacinth Bucket in the British comedy series Keeping Up Appearances. Poor Hyacinth goes to great lengths to give the impression of gentility, only to succeed in being comically genteel.
In terms of language, a genteelism is a word or turn of phrase that a speaker thinks is more refined than the usual word or phrase: pugilist for boxer, expectorate for spit
The incorrect use of “I” for “me” in such constructions as Give the book to Jane and I probably originated as a genteelism. It has been used so frequently on television, however, especially on soap operas, that many speakers simply parrot it, imagining that it must be correct because they’ve heard it so often.