I rarely bother to deep fry fries. I buy them precut, blanched and frozen in the supermarket and bake them in the oven. If I bake them as intended, they are fluffy on the inside. If I forget them in there for about double the time, they become harder and crispier throughout.

I don't think you can imitate this with a fryer only, because you need a certain temperature there, else the fries soak up the oil. So maybe do your one-minute fry first, then put the drained fries in an oven for as long as it takes. Or just start with the convenient prepared kind and use the oven from the beginning.

Normally, French fries are cut thick. To make whole crunchy French fries, just cut them as thin as you can.

The crosscut of ordinary French fries is about 1 cm (0,4 inch), you can make 1 mm crunchy fries. I propose you test different widths and report back on your findings.

Cook them thrice

The trick to crispy fries is to remove moisture. I highly recommend trying this recipe by Heston Blumenthal. I'll provide a short description, but you should really follow the recipe when you're trying this method.

The first cook is in water (I assume to remove starch and get them softened already), the other two follow roughly the double fry idea.

The important parts are in-between cooks. Rather than just letting them cool off on their own, you put them in the freezer (after cooling). That helps remove even more moisture from the fries which makes the final product crispier.

_{Side-note regarding temperature: You really shouldn't be frying potatoes above 180 degrees Celsius or 356 degrees Fahrenheit. While deep frying always produces acrylamide which is carcinogenic, frying at temperatures higher than that causes needlessly high levels of the stuff. For more information, see this page by the American Cancer Society.}

I once got the advice to double-fry them at different temperatures:

1. First you fry them for 5-7 minutes at 325F / ~162C
2. Then you remove the fries from the oil, increase the oil temperature to 350F/~175F, and fry them for another 2-3 minutes until golden & crispy.

It is best to soak the potatoes in cold water before frying to remove the excess starch.

Guy Fieri shares his pro advice on double-frying here.

"Potato Sticks" are made but a combo to @BaffledCook and @rumtscho's answers, to cut the potatoes into matchstick sizes. Using a mandolin with a small size may be the easiest way to get a reasonably uniform cut. Deep fry batches in hot oil. Blot excess oil, and add salt or desired spices and put into a pre-heated oven while you do additional batches. The longer you bake, the more crisp through. Larger cuts will tend to take longer and be more prone to soft in the middle. Small batches with reduce temp drops in the oil which would promote a tend to soggy spuds. It can work with larger cuts, so you would want to experiment for exactly the results you want.

My fries always come out crispy and I want them fluffy on the inside. Here's how I do it. First, I use Russet or Idaho potatoes. Then I use a mandolin to cut them into "small fries." That is, fries about the size of MacDonald's fries, not larger. I immediately put them in ice water. While they are chilling out (pun intended), I heat up the oil, usually canola or peanut oil to over 350 degrees, usually not over 375. Then I drain and dry the potatoes. I use a clean kitchen towel to dry them. I put the fries in the oil a handful at a time to maintain temperature. When they are all in, I fry them until crispy. As I said, they turn out crispy all the way and not fluffy on the inside.