If you are talking to someone who understands cooking, you can use the verb french:
- To cut (green beans, for example) into thin strips before cooking. (The Free Dictionary)
So you could say "You should french these cucumbers". (This is apparently an American usage and should probably be avoided in other regions.)
Technically speaking, french fries are in the shape of a parallelepiped:
A solid with six faces, each a parallelogram and each being parallel to the opposite face. (The Free Dictionary)
But that's not very useful in ordinary conversation, and doesn't define the ratio of the sides (long & thin vs. short & fat); if you don't want to use the verb french, simply describing the shape as you have ("long, flat strips") or as the dictionary has ("thin strips") should suffice, so you could say "cut the cucumbers into long, thin strips"; or, since french fries are a very well-known item to begin with, you could say "cut the cucumber into french fry-shaped pieces."
However, as french fries do come in different shapes and varieties (shoestring, steak-cut, waffle-cut, wedge, etc.), you may actually want to be even more specific and give actual dimensions: "Cut the cucumber into long, thin strips approximately 1/4-inch square and 2 to 3 inches long."