The Character of James Potter
I think James Potter only listened to Sirius Black out of all other people. We saw that multiple times in SWM where James listened to Sirius.
Potter's one of the issue was his blind trust in his friends especially Sirius over the others. It was Sirius who got him to suspect Lupin being potential traitor spy and it was Sirius who's suggestion actually made sense if Peter wasn't a traitor.
As for the assumption that Potters wouldn't have died if they made Sirius secret keeper, I disagree with it, @darkangel and @thegestaltprince.
Sirius made it very clear that him being the secret keeper was quite obvious and one of the reason for his suggesting Peter. In case he remained keeper, I can count on one hand many scenarios where Peter would've engineered a trap for Sirius leading to his capture by Death Eaters.
What we know about Fidelius is that it's secret couldn't be divulged by torture. But other thing which you should know is that while secret keeper is only one who can tell the secret even if it's known by others, in the event of his death, the others knowing the secret become new secret keeper or keepers.
In canon, the secret keeper of Grimmauld Place was Dumbledore following which Moody told Harry that they all became keepers after Dumbledore's death which included Snape and that's why he put tongue tying curse.
A secret keeper Sirius would've told secret to his close friend Peter and after his death, Peter would've become new secret keeper and events would've gone similar to canon, difference being no Sirius Black who is now dead.
