GerFrUK and "I Won't Say I'm in Love" from 'Hercules' by Megara (Susan Egan)?
Hmmm...It is very fitting for these three. Especially when I have Fruk already established and Arthur is left to deal with also having a crush on Ludwig but not wanting to change things because he finally feels secure in his relationship with Francis, why complicate it more. But Fran also has a crush on Ludwig and encourages Arthur to also pursue Ludwig with him.
But as for a specific au? Let's see. Going off the whole Greek God thing...Maybe a God AU (not Greek specifically though). Arthur is the God of Destruction, Francis the God of creation and though in their roles they represent a balance, their personalities clash so they have a rivalry for centuries. Yet at the same time, there were times of peace, quiet times where they found common ground and slowly, they also started to love each other leaving all the other Gods to place bets on when they'll finally kiss.
Eventually the two get together after a fight finally turns into a make out session. They still bicker and fight, but they always come back to each other.
Arthur likes to mingle amongst the mortals. He always loved a good tavern/pub scene despite being an immortal deity. When he and Fran get together, Fran joins him on these excursions. On these excursions they start to meet frequently with a particular tavern/pub owner, a German fellow named Ludwig (he's actually a co-owner with Gil but Gil doesn't play a huge part in this). He was awkward and intimidating at first, but it was a great place to get a beer. The two Gods eventually discover Lud isn't really a scary standoffish guy, he's just isn't the best at socializing.
Both Fran and Art start to fall for him, but Arthur isn't exactly great with longstanding relationships. He's had flings with Gods and mortals alike. Last long term relationship resulted in a fractured friendship and he's rather not go through something like that again. Plus he's a mortal, that's going to lead to heartbreak. He's comfortable with Francis, why ruin it? Francis, ever the romantic can tell Arthur has feelings for Lud and also having feelings suggest they pursue him. Arthur is at first against it, but eventually Francis gets him to give into his feelings and agree to court him.
They all started dating and live happily ever after. Francis being the God of creation can probably pull strings and get Lud to be immortal so they don't have to worry about that. And yeah!
