How could I make stuffed french fries?
So I have a method that I just worked out but it is insanely labor intensive and only suited to small batches.  With that said, here you go. Also, steps will be slightly out of order so make sure you read completely through.

To create filled french fries:

First, you need to cut your potatoes into slightly larger fries than normal. You are looking for about 1/2 to 2/3 of an inch on each side.   You need to preheat your grease to 275. Once your grease has preheated, parcook the french fries.  They should be cooked but not crisped or browned. Lay fries in a layer on a pan and place into fridge. Prepare your injection.  I used sour cream but you can add whatever you want. (I thinned the sour cream down with a little milk till it got to the consistency that I wanted) Load your injection into a syringe and inject into the now cooled but not cold fries. Don't over-inject or you will ruin fries left and right. Inject by running the needle fully in, then slowly removing while slowly deploying the filling. As you inject, lay on a pan in the freezer. This is important because you need to get the fries frozen as quick as possible.

While you wait, prepare your seasoned flour.  I tried some with out the flour and the fries tended to lose the filling.  Your are going to be working the fries in small batches.  It is imperative that the fries be frozen through, if they aren't you will lose your filling.  Toss a handful of fries into the flour and coat thoroughly.  Alternately, you can coat fries in an egg wash then flour, but the results were a little too far from traditional fries for me. Toss the fries into 375 degree oil until fries brown and are crisp on outside.  You need to watch carefully and as soon as they start floating count to ten then remove. You can't over cook them or you will not have any filling remaining.

A couple of extras:
I don't know how a filling that is predominately water will work in these, but I would conjecture very poorly given how fries cook.

Your hole in the potato is only going to be sealed with flour so you might see some leakage. I couldn't figure out a way around that.

You benefit from the freezing with a much improved bite texture over my normal fry prep.

The final result has a high wow factor, and was pretty tasty. I am not sure the results are worth the effort, but I think if you try a high flavor filling it will go a long way to making it worth while.