I don't know why Saint Francis did what he did, and neither do you. In answer to your question, yes he would have been a demonstrably better man if he did all those good things with no consideration for whether there was a god or not -- because he wouldn't have been operating in a reward/punishment scenario. What I do know is that it's very probable that the fear of being tortured for eternity influenced his decision making process, as well as the desire to be rewarded with eternal life.
Surely you can see the difference between doing a good deed for the sake of it's goodness vs. doing a good deed for the sake of its goodness AND to avoid eternal torture AND to receive the reward of eternal life.
You still haven't answered my question.