For the purposes of priority in making a blessing, is a french fri considered a shalem food or is it considered a broken piece of potato?
The reason "Daver Shalem" gets priority can be for one of two reasons
1) The food item was created that way ("ברייה") an example could be a apple or even a grape.
2) That by taking the "Daver Shalem" before the other item you are beautifying the mitzvah of making a bracha (Hidur Mitzvah) Thus if you had a large slice of bread and a small roll you would make the bracha on the roll since that has an advantage of being "shalem" (Think of a formal meal like a wedding. Normally a roll is put in front of each person not several slices of bread since the roll is more esteemed ("mechubidik"*??) )
Since a french fry on its own while technically "shalem" was a) not created that way b) a single french fry is not considered more esteemed to serve over a piece of potato I would say that it does not take any preference over the broken potato based on shalem**.
* mechubidik - apologies for the "yeshivish" but a good translation escapes me at the moment. MY editors please suggest an appropriate translation.
** there may be a case to say that in this case you would go for the bigger of the 2 items but I haven't seen that specifically brought down.
Yerushalmi Perek 6 Halacha Aleph
SA 168:1 + Mishna Berurah
There is a trick that you can do on Yom Tov whereby you can take a broken piece of matzah, and burn the broken edge, rendering the piece whole for the purpose of lechem mishna.
Since the fry is surrounded on all sides by crust, I would say that it would be whole just like the formerly broken matzah.