Potatoes with different flesh colours contain health-promoting compounds, i.e., hydroxycinnamic acids, which vary in content and stability during thermal processing. The aim of this study was to determine the effect of the technological stages of the production of French fries obtained from potatoes with different flesh colours on the content of selected hydroxycinnamic acids, as well as the stability of these acids, their percentage in sum of acids, total phenolic content and antioxidant activity (ABTS, DPPH) in semi-products and ready-to-eat products. During the production of French fries, samples of unpeeled, peeled, cut, blanched, pre-dried and fried potatoes were collected. After peeling, coloured potatoes, especially purple ones, had more hydroxycinnamic (5-CQA, 4-CQA, 3-CQA and CA) acids remaining in the flesh than in the flesh of the light-yellow variety. The greatest losses of the determined hydroxycinnamic acids, regardless of the given potato’s variety, were caused by the stage of pre-drying (about 91%) and frying (about 97%). The French fries obtained from the potatoes with coloured flesh, especially those with purple flesh, had the highest amount of stable 5-CQA and 4-CQA acids as well as 3-CQA acid, already absent in light-yellow French fries. The least stable acid was CA acid, which was not found in any of the ready snacks.