Jeuno fame is a rough average of your fame in the other three starting nations. If you further raise your fame there, it will in turn raise your fame in Jeuno.
This grants Jeuno fame directly and is repeatable, though when I was raising my Jeuno fame, I'd often forget to go until it was too late.
If you want a cheap and easy way to raise your fame in the 3 starting countries, try:
Selbina for Bastok and Sandy fame. or
Windy which requires Bastok to be in 1st or 2nd place in conquest.