UPDATE (11/23/15): Per ISU's official announcement, the Grand Prix Final qualification will be amended as follows:

As expected, the short program standings will be used as the final standings.
Six skaters/teams in each discipline will qualify based on the normal criteria, except the tiebreak procedure for qualification has been amended.
If a skater or team is the first substitute (7th in the overall standings) AND skated the short program at Trophee Eric Bompard, he/she/they will qualify as well.

The last bullet is contrary to what we had interpreted, which was that there would definitely be seven entries in each discipline. As such, disciplines could still have just six entrants if the first substitute did not compete in Bordeaux. Given the circumstances, this does seem to be the fairest and most optimal outcome that is economically and logistically feasible.

So what does this mean based on current standings for the Bompard competitors? For a full analysis and current qualification standings, have a look at this analysis.

Patrick Chan is currently third in the standings, and with just NHK Trophy left, it looks to be mathematically impossible for him to not make it to the Grand Prix Final, even without the 7th place bye.
Gracie Gold is assured a Grand Prix Final spot after her first-place short program turned into a first-place standing.
Things look a lot less rosy for Elizaveta Tuktamysheva, who is currently fifth in the standings, especially with Mao Asada, Ashley Wagner, Satoko Miyahara, and Anna Pogorilaya at NHK. It is, however, still mathematically possible for her to make it to GPF, she will just need some unexpected outcomes for that to happen. The same goes for Julia Lipnitskaia, who is sixth in the standings. She will need a whole lot more craziness to happen for her to make it to Barcelona.
In pairs, Julianne Seguin/Charlie Bilodeau and Cheng Peng/Hao Zhang are in fourth and fifth in the standings, respectively. Seguin/Bilodeau have an outside short, but Peng/Zhang look like they will finish just outside seventh place. Perhaps the biggest surprise are Vanessa James/Morgan Cipres, who were second in the short and have a solid shot at making it to Barcelona, especially with Tatiana Volosozhar/Maxim Trankov out of NHK.
This official amendment to the competition means that, Volosozhar/Trankov will definitely not make it to the Final by virtue of only one short program at one competition.
For dance, Piper Gilles/Paul Poirier were second at TEB are in fifth overall, with an outside chance of making it to the Final. But Madison Hubbell/Zachary Donohue, who were first at TEB, would make it the Final with as low as fourth at NHK because of the win and the tiebreak rules.

View image | gettyimages.com

After Trophee Eric Bompard was cancelled midway through the competition as a result of the terror attacks in Paris, Russian sports media reports that the International Skating Union has settled on the following to change the Grand Prix Final criteria , or at least the way I interpreted it from the translated article:

The short program standings from Bompard will be used as the final standings, and six skaters/teams in each discipline will qualify as normal
A seventh skater/team in each discipline will be chosen (?) from Trophee Eric Bompard

The original proposal from Russia's figure skating federation was to add two entries per discipline, but it looks like the final decision it to add one.

Note that official ISU communication about this change has not been posted yet. We will await news directly from ISU before providing final confirmation. But if my interpretation is correct, this basically provides an outlet for the Chans, Tuktmyshevas, Golds, and Volosozhar/Trankovs of the world to get to the Grand Prix Final without officially qualifying. While both Gold and Volosozhar/Trankov skated well in the short, Chan and Tuktamysheva did not, which put their qualifying hopes in the balance.

Withdrawals galore
Speaking of whom, Tatiana Volosozhar/Maxim Trankov have decided to withdraw from NHK Trophy next week, but this change of rule for the GPF could very well mean that they get to go to the Final anyway. We'll see. Volosozhar has a foot injury that she's trying to rest and heal. They have been replaced by Great Britain's Amani Fancy/Christopher Boyadji.

At this week's Rostelecom Cup, we have already had withdrawals from Alexander Majorov and Peter Liebers (ongoing adductor injury) from the men's event. And we just heard that Alexandra Paul/Mitchell Islam will be withdrawing from NHK as well next week. They will be replaced by Anastasia Cannuscio/Colin McManus.

And most recently, U.S. champ Jason Brown is no longer on ISU's list for next week's NHK Trophy. He is recovering from a back strain that happened during practice. No replacement has been named.