I'm just wondering. I like experimenting with French toast recipes. What is the best ingredient to add to a normal French toast recipe to make it taste pumpkin flavored?
Not meaning this as a snippy answer at all, but I would say: pumpkin.
I would suggest substitute pumpkin bread and continue as normal. This one I have done before. It is a heavier French Toast (or eggy bread, pain perdu or many other names around the world), but turned out quite nice in my opinion.
Another option would be a stuffed version with pumpkin as the stuffing. And also coming to mind would be a pumpkin butter or compote topping on a recipe you already use.
If you are willing to invest the effort in making your own yeast bread, challah with pumpkin is a traditional Sephardic bread. Here is a recipe from Maggie Glazer's A Blessing of Bread which I have made dozens of times and it has always turned out great. We usually eat all of it before it is ready for French toast, but I've done French toast with it a few times and they've been great as well.
Canned pumpkin -
which isn't really pumpkin, but it's [is] more pumpkin than pumpkin.
(I don't know your location, and whether canned pumpkin is available, so I hope this is an answer for you.)
Also, I think that most interesting way to do this would be to use a filling and make a stuffed french toast (as dlb suggested). Since I don't think the filling will really cook, I would not use a custard based one (like a pumpkin pie). I would probably take a can of "pumpkin", reduce it a bit in a saucepan, add pumpkin pie spice to it (and maybe a bit of sugar or honey), let it cool some, and then add in some cream cheese and mix into a spread. Spread the mixture between two pieces of staled (or lightly toasted) bread, and then dunk the whole thing in the egg wash.
Actually, I might just go and try that myself!
ETA: I had read / heard / seen that 'canned pumpkin' was made of squashes because the legal definition of pumpkin was different than our expectations. While that (the legal definition) may be true, I was today years old when I found out that Libby's uses something that looks like a hybrid (and is a cultivar), but is classified as a pumpkin, and not a squash, by agricultural trade groups.
While I agree that pumpkin bread would be the first best choice, I do also suggest as a second choice if you do not have that bread that when you make you custard you include some pumpkin in the custard.
If you are making a dipping mix beyond the old motherly milk and egg mixture, you will know that there are many other french toast makers that actually prepare a custard with eggs, dairy, extract, sugar, cinnamon, sometimes zest and even some juice of an orange, and so on, considering there culinary creativity.
Do the same, but try adding a tablespoon or two of canned pumpkin to your mix. Save the argument of whether canned pumpkin is 100 percent pumpkin, blah, blah, blah...and just accept it is our familiar version of pumpkin most of our life. Start small, to ensure how it cooks(i.e. doesn't burn) and tastes. Since there is no such thing as pumpkin extract, I think this is your only other option.