The answer to this question depends on how strict of a vegan you are.
That might sound weird, but it’s pretty clear when we look at the nutritional information and ingredients for fries at Wendy’s:
Potatoes, Vegetable Oil (Contains One Or More Of The Following Oils: Canola, Soybean, Cottonseed, Sunflower, Corn), Dextrose, Sodium Acid Pyrophosphate (To Maintain Natural Color). Cooked In Vegetable Oil (Soybean Oil, Vegetable Oil [May Contain One Or More Of The Following: Canola, Corn, Or Cottonseed], Hydrogenated Soybean Oil, Dimethylpolysiloxane [Anti-Foaming Agent]. Seasoned With Sea Salt. COOKED IN THE SAME OIL AS MENU ITEMS THAT CONTAIN WHEAT, MILK, AND FISH. Salt: Sea Salt.
The actual fries themselves consist of potatoes and a ton of different vegetable oils, all of which are vegan. Side note: Dimethylpolysiloxane is an ingredient derived from silicon in an industrial process, which is also vegan.
I highlighted the big potential issue, which is that Wendy’s reuses oil from other menu items to cook their fries.
If you’re vegan because of allergies to milk or fish, you probably don’t want to take the chance of your fries being contaminated.
Likewise, if you’re a very strict vegan, you may not consider them vegan.
I think that most vegans would say that the microscopic (if any) amount of dairy or fish here isn’t too big of a deal and that Wendy’s fries are vegan for most vegans.