I don't think it's possible to get a Burgundian Inheritance under a France PU. I tried several times after I got a freak Spain PU while holding France.
First of all, if Burgundy rivals you, they won't let go because of Calais.
Second, if they don't rival you, you also need them to not rival France, which I've never seen happen... statistically it's possible but... no.
So in both those cases it goes to Austria.
If you've already got France under a PU, I can't see it going to France anyway because they're no longer a contender (not sure, just my best guess)
Has anyone tried declaring on Burgundy and holding their provinces until the inheritance happens? I did this once, but didn't have their capital yet and when the inheritance triggered, it went to Austria who immediately wiped me off the continent.
These days, I prefer eating them all a few provinces at a time anyway.