In The Godfather Part 1 (I haven't seen Parts 2 or 3 yet, if they're relevant) it's seen that The Corleone family does a lot of "favors" for Johnny Fontane - as was explained early on in the film - and the Wikipedia page
* They got him out of his original contract
* They got him into his desired role in Woltz' movie
* They got him the Academy Award for Best Actor
* They funded his own film studio
I didn't see the last 2 favors in Part 1, but I assume they're in Part 2.
It is shown that Fontane is Vito Corleone's godson - which effectively makes him extended family - and when you're family you get favors "for free" to an extent but these are tall-order favors. We do see Fontane thank Vito by way of a delivery of a bouquet of balloons and flowers - which Vito is dismissive of and instructs his henchmen to dispose of it, which suggests to me that Vito doesn't think highly of Fontane - or at least is ungrateful of this token of appreciation.
Furthermore, in the scene where Fontane asks for his second favor that Vito is clearly disappointed or otherwise annoyed in Fontane's apparent learned helplessness and seems to resent having to undertake his request.
Given this, why does Vito do these favors at all? What is in it for the Corleone family for helping Fontane? They already have enough friends in high-places that pushing Fontane into higher celebrity status wouldn't be worth the potential risk of negative attention that the limelight can bring. I also note that Woltz is very well-placed himself (after all, he has power over Fontane), it makes more sense to me for the Corleones to get-friendly with Woltz than to intimidate him instead - even if it means letting Fontane down this one time.
I note that it is possible that the family is getting a cut from Fontane's income, which is presumably substantial, but this never touched-upon in the film - and if they were it would be insignificant compared to what the rest of their criminal enterprise brings in.
It's shown at the start that Vito works on, at least, a favors-for-favors basis, that if he does something for you he will call in the favor from you at an unspecified point in the future - but we never see that happen with Fontane.
So what's in it for the Corleones to help Fontane?