Conformation traits such as joint angles are important selection criteria in equine breeding, but mainly consist of subjective evaluation scores given by breeding judges, showing limited variation. The horse shape space model extracts shape data from 246 landmarks (LM) and objective joint angle measurements from triplets of LM on standardized horse photographs. The heritability was estimated for 10 joint angles (seven were measured twice with different LM placements), and relative warp components of the whole shape, in 608 Franches-Montagnes (FM) horses (480 stallions, 68 mares and 60 geldings born 1940–2018, 3–25 years old). The pedigree data comprised 6986 horses. Genetic variances and covariances were estimated by restricted maximum likelihood model (REML), including the fixed effects birth year, age (linear and quadratic), height at withers (linear and quadratic), as well as postural effects (head, neck, limb position and body alignment), together with a random additive genetic animal component and the residual effect. Estimated heritability varied from 0.08 (stifle joint) to 0.37 (poll). For the shape, the type was most heritable (0.36 to 0.37) and evolved from heavy to light over time. Image-based phenotyping can improve the selection of horses for conformation traits with moderate heritability (e.g., poll, shoulder and fetlock).