Apparently not. Based on my experience, you can get an AF award from Delta, using your Delta miles. It's just a different code than the Delta awards. In my case, the award codes are VF21 and VF22, both AF awards, apparently, because we are taking an AF flight in the middle of our vacation.

What happened is you can't use a Delta award to book a flight operated by AF, even if it's a code-share. Not a big deal, really, but nice to know.

Bruce