frank (n.)
short for frankfurter, by 1916, American English. Franks and beans attested by 1953.
Frank (n.)
one of the Germanic tribal people (Salian Franks) situated on the lower Rhine from 3c. that conquered Romano-Celtic northern Gaul c.500 C.E.; from their territory and partly from their language grew modern France and French. Old English franc, franca "freeman, noble; Frank, Frenchman," from Medieval Latin francus, a Late Latin borrowing of Frankish *Frank, the people's self-designation (cognate with Old High German Franko, the Latin word also is the source of Spanish and Italian names Franco).

The origin of the ethnic name is uncertain; it traditionally is said to be from the old Germanic word *frankon "javelin, lance" (compare Old English franca "lance, javelin"), their preferred weapon, but the reverse may be the case. Compare also Saxon, traditionally from root of Old English seax "knife." The adjectival sense of "free, at liberty" (see frank (adj.)) probably developed from the tribal name, not the other way round. It was noted by 1680s that, in the Levant, this was the name given to anyone of Western nationality (compare Feringhee and lingua franca).
frank (v.)
"to free a letter for carriage or an article for publication, to send by public conveyance free of expense," 1708, from shortened form of French affranchir, from a- "to" + franchir "to free" (see franchise (v.)). A British parliamentary privilege from 1660-1840; in U.S. Congress, technically abolished 1873. Related: Franked; franking. As a noun, "signature of one entitled to send letters for free," from 1713.
frank (adj.)
c. 1300, "free, liberal, generous;" 1540s, "outspoken," from Old French franc "free (not servile); without hindrance, exempt from; sincere, genuine, open, gracious, generous; worthy, noble, illustrious" (12c.), from Medieval Latin francus "free, at liberty, exempt from service," as a noun, "a freeman, a Frank" (see Frank).
Frank, literally, free; the freedom may be in regard to one's own opinions, which is the same as openness, or in regard to things belonging to others, where the freedom may go so far as to be unpleasant, or it may disregard conventional ideas as to reticence. Hence, while openness is consistent with timidity, frankness implies some degree of boldness. [Century Dictionary]
A generalization of the tribal name; the connection is that Franks, as the conquering class, alone had the status of freemen in a world that knew only free, captive, or slave. For sense connection of "being one of the nation" and "free," compare Latin liber "free," from the same root as German Leute "nation, people" (see liberal (adj.)) and Slavic "free" words (Old Church Slavonic svobodi, Polish swobodny, Serbo-Croatian slobodan) which are cognates of the first element in English sibling "brother, sister" (in Old English used more generally: "relative, kinsman"). For the later sense development, compare ingenuity.