Climate change is projected to amplify existing climate-related risks and create new risks for natural and human systems. Perennial forage species may represent a valuable alternative to annual forage crops by improving the environmental and economic sustainability of Mediterranean agro-pastoral farming systems through a reduction in soil erosion and the conservation of soil water. Under climate variability, a multi-environment experiment was conducted in Morocco under three contrasting environments—Annocer, Guich, and Tassaout—over three consecutive years (2013/214, 2014/2015, and 2015/2016). Measurements for productivity traits and summer dormancy were taken for 21 genotypes, 18 of which were (F1 hybrids) generated between two varieties of cocksfoot—Dactylis glomerata ssp glomerata and Dactylis glomerata ssp hispanica—with different ranges of senescence, parents, and Ludac values (temperate control). An evaluation of the stability and adaptability of the cocksfoot genotypes was established by AMMI (Additive Main Effects and Multiplicative Interaction) using some productivity traits (plant height, annual dry-matter production, and spring biomass) and summer dormancy to determine differences between genotypes across environments. The present study aimed to identify the effect of environmental control on the induction of summer dormancy and identify genotypes with both mean performance and high stability. The results indicated a large variability among genotypes from year to year and location to location. The Analysis of Variance (ANOVA) showed highly significant differences (P < 0.0001), which were recorded between genotypes for all measured traits, mainly due to changes in genotype rankings. Significant effects of genotype, environment, and GxE were noted. Moreover, significant correlations (P < 0.0001) were obtained between environments. Env2 and Env3 achieved the highest mean annual dry matter.