Faced with the challenges posed by climate change, Serbian viticulture is looking for sustainable solutions for adaptable production. This study shows that grass is a multifunctional tool for overcoming the challenges of intensive viticulture while maintaining the quality of the grapes. In a three-year research experiment (2020–2022), the maintenance of an inter-row sward in a vineyard with four certified high-quality French Cabernet Sauvignon clones was investigated, and its effects on the ampelographic composition of the grapes and the quality of the grape juice (must) were studied as a function of wine quality. A grass sward was established between the rows as a biological soil management system and as a climate change adaptation measure in a high-intensity viticultural system. A grass–legume mixture was used as an inter-row cover crop, with nitrogen applied in two doses (50 and 100 kg ha−1) in spring. The growth of the grasses responded to the nitrogen fertilisation, which was reflected in the biomass production, surface cover and nitrogen content in the biomass. At the end of the study, the biomass of the grass increased threefold when a high dose of nitrogen was applied compared to the non-fertilised grass. In contrast to the effects of nitrogen on the sward, N has no effect on the quantitative or qualitative parameters of the grapes. Clone 169 was separated for most grape mechanical parameters such as the bunch mass, all berries and the bunch stem; clone 15 showed the best grape juice quality parameters such as the sugar content and glycoacidometric index. The results show an option for climate change adaptation in viticulture that can mitigate the effects of rising temperatures, contribute to soil conservation and carbon storage in biomass and enable timely interventions in vineyards after heavy rainfall by creating accessible paths within the vineyards. The three-year effect of the different nutrient management of the sward in the inter-rows of Cabernet Sauvignon showed that the interaction between the two systems, sward and vine, is low and has no negative impact on the ampelographic and qualitative grape parameters.