Viticultural byproducts are known to contain high-value compounds such as stilbenes. The wine sector in Savoie Mont Blanc region (France) generates a great amount of waste, including grape canes and grapevine stocks that remain unvalued. Herein, the potential of the most widespread grapevine varieties in the Savoie Mont Blanc territory, Jacquère and Mondeuse, as sources of two stilbenes, trans-resveratrol (Rsv) and trans-ε-viniferin (Vf), was investigated for the first time. Using the reported extraction technique, the present work focused on several pre-extraction parameters influencing the extraction efficiency, including grapevine variety, age of vines, time of material storage, and particle size of the woody material. This work revealed important Rsv and Vf contents in Jacquère residues of 1681–6124 and 1620–6667 mg·kgdw–1, respectively, whereas for the Mondeuse variety, the targeted molecule yields were 1724–4636 and 1713–5322 mg·kgdw–1, respectively. These results are promising when compared with the well-known high stilbenes levels in Pinot Noir and Gewurztraminer varieties but also highlight a considerable variability depending on the applied pre-extraction parameters.