European larch is an ecologically and economically important tree species planted across a wide range of environments. Understanding its response to the rapidly changing climate is essential to developing efficient gene resource management strategies in line with the assisted migration methodology. In this study, we quantified the genotype x environment interaction (GxE) of a larch provenance in a multi-environmental trial analysis using factor analytic (FA) modeling. We analyzed the mean annual height increment (MAI-H), the mean annual diameter increment (MAI-DBH), and wood density (PP). Additionally, we evaluated the effect of several environmental variables on these traits. The genetic correlations between sites varied from −0.53 to 0.99, −0.87 to 0.99, and −0.17 to 0.99 for MAI-H, MAI-DBH, and PP, respectively. This indicates the presence of low to high GxE. The growth traits showed more GxE signal than wood density. Narrow-sense heritability estimates were 0.41, 0.16, and 0.35 for MAI-H, MAI-DBH, and PP, respectively. The FA modeling of order 2 explained 77.4%, 67.9%, and 77.3% of the genetic variance for MAI-H, MAI-DBH, and PP, respectively. For MAI-H, the latent regression plots for the predicted site means indicate a significant positive correlation with the first factor loading. At the individual genotype level, the latent regression plots indicated high levels of GxE, especially for growth traits. Significant and relatively high correlations were found between several EVs and the factor loadings of the FA models, suggesting their possible influence on the genotypic performance across environments. Regarding MAI-H, elevation, averaged monthly mean temperature, precipitation seasonality, and stand age were correlated with the first factor loading. Annual temperature range with both the first and second factor loadings. For MAI-DBH, the mean diurnal range was correlated with the first factor loading. In the case of PP, we found that elevation was correlated with the second factor loading. Overall, this approach successfully modeled the GxE and identified environmental variables likely affecting it. Therefore, we conclude that this methodology is a valuable tool for selecting suitable genotypes adapted to specific environmental conditions.