There are two little dogs! There’s the one near the couple and a second one on the track off to the right, leading into the woods. Here:
Detail of the May calendar image Morgan Library MS H.8_fol._3r
I don’t think the two dogs are the same breed; the one in the trees is more hound-like. It looks to me like the couple in this scene is the courting couple featured in the April calendar image, picking flowers and making garlands. The trees look as if they’ve been pollarded, the lower limbs removed to allow for easier passage (and for burning), and to make it easier to gather nuts.
Ms. 65 f. 5v Musée de Condé, Chantilly, France by the Limbourg brothers c. 1411–1416 Image: R.M.N. / R.-G. Ojéda, Wikimedia Commons
This is the May calendar page from the Très Riches Heures de Jean Duc de Berry. It shows one of the more popular labors of May, a May day outing or jaunt. This is the aristocratic version of bringing in the May, with richly dressed aristocrats on very fine horses, wearing May garlands, traveling with servants, including musicians. In the background is the Hôtel de Neslé, one of the Duke’s Paris residences, and the Conciergerie and the Tour de l’Horloge on the isle de la Cité,much as they look today. Notice the details of the two little dogs in the foreground, and the flowering shrub. I suspect, but can’t prove, that the horses as well as at least some of the riders, would have been known to the Duke. Various scholars have suggested that the gentleman in front with the garland and the very fancy robe with gold embroidery is the Duke himself, perhaps looking at his bride-to-be on the white horse. It is also interesting that three of the women are dressed in green, the color of spring, and of fairies.