Whether or not the proposed itinerary is a "legal" connection or not [I can't see why it would be deemed illegal, but I can easily see FB objecting to the mixed-carrier aspect, and the repeated transfer through a single point], I foresee immense difficulty even just having availability pop up on ALL sectors when queried for such an itinerary.
Note that, in the "Award booking issues on FB website" it has been noted that no bookings are currently possible on SB - with one poster blaming recent blog posts.
Air France does indeed seem to be hostile towards FB members who use their account without ever having earned miles by flying - we have had a few reports on here down through the years (and there are mutliple blog posts) about people having tickets cancelled and/or accounts audited after making bookings with credit card transferred points.
Try ringing the US call centre (who don't have a great reputation, from what I have read on here) and please report back.