The potato is probably not as important as the method. Simply frying them will not get you the fry you want. Basically you boil them, then double fry them. Here are the steps for The Perfect French Fry:
Ingredients
2 pounds russet potatoes (about 4 large), peeled and cut into
1/4-inch by 1/4-inch fries (keep
potatoes stored in a bowl of water)
2 tablespoons distilled white vinegar
Kosher salt
2 quarts peanut oil
Procedure
Place potatoes and vinegar in saucepan and add 2 quarts of water and
2 tablespoons of salt. Bring to a boil
over high heat. Boil for 10 minutes.
Potatoes should be fully tender, but
not falling apart. Drain and spread on
paper towel-lined rimmed baking sheet.
Allow to dry for five minutes.
Meanwhile, heat oil in 5-quart Dutch oven or large wok over high heat
to 400°F. Add 1/3 of fries to oil (oil
temperature should drop to around
360°F). Cook for 50 seconds, agitating
occasionally with wire mesh spider,
then remove to second paper-towel
lined rimmed baking sheet. Repeat with
remaining potatoes (working in two
more batches), allowing oil to return
to 400°F after each addition. Allow
potatoes to cool to room temperature,
about 30 minutes. Continue with step
3, or for best results, freeze
potatoes at least over night, or up to
2 months.
Return oil to 400°F over high heat. Fry half of potatoes until crisp and
light golden brown, about 3 1/2
minutes, adjusting heat to maintain at
around 360°F. Drain in a bowl lined
with paper towels and season
immediately with kosher salt. Cooked
fries can be kept hot and crisp on a
wire rack set on a sheet tray in a
200°F oven while second batch is
cooked. Serve immediately.
Worth reading is also the science behind the perfect 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.
Best Answer
Good Eats(Alton Brown) has some good descriptions of the various difference's between potatos. He has an episode dedicated to potatoes. Main thing is the starch content in them. He has an example of each of the three groups (High, Medium, Low), includign a brief description and sample application. He mentions mentions frying in the High Starch content group, specifically Russets. He then has another episode simply about frying, where he actually talks about French Fries and again mentions the Russet (High Starch).
While you can make fries out of different types of potatoes (some of the more "all purpose" potatoes), if you want a really good classic french fry, you're going to want to look for a Russet, with a similar starch content.
Here's a page that lists some of the more common varieties. Maybe you can look to see what you bought? The age will probably affect it. A younger potato will in fact be sweeter
So, to answer your specific questions. I'm betting you did in fact buy a potato. It's probably just a sweeter variety. If it doesn't say at the market where you bought it what kind they are, I'd ask the people who work there. Also, look at the third link I have above, it does have a few pictures as well as good descriptions on what they look like.