The verb franchir means to go across some limit, either a physical obstacle like a wall or gate, or a metaphorical boundary like a city line or national frontier. It can also mean to break some social norm, or cross some notable threshold like a $100 a barrel for oil.
The verb affranchir means to give someone or something their independence, to free a serf, or a slave, or a colony. The reflexive form s’affranchir can also mean to free oneself of a constraining condition – fear of flying, or living according to societal norms.
Confusing, right?