Methink the Bayard Knight is a possible way but the most probable explanation is the one linked to Bayard the Mythological Horse for the following reaons :
- Famous legendary episodes involved the 4 Aymond Brothers riding the horse all together but the whole legend is wide in time and space, and included other riders, mythological or historical, including Renaut the Montauban, as you said, but also the wizard Maugis d�Aigremont, Astofle, Roland (main character of the world famous � song of Roland �) and even Charlemagne himself. So if the most famous representation of the horse in Belgium shows it with 4 riders (famous local episode), other representations existed and exist.
- The Legend of Bayard the Mythological horse was strong in most parts of today�s south Belgium, but especially in the Liege area and along the river Meuse; many episodes of the myth occured in that area (including the famous attempt of Charlemagne to drown the Horse into the River Meuse) so lots of places are named after the Myth of Bayard (lots of places where the horse is supposed to have marked the rocks/ground with one of its mighty feet, etc.). It seems it was a famous character in popular culture. Charlemagne himself, which plays a major role in the legend of the horse, is supposed to be born in that area too.
- Pierre Terrail the Bayard lived in the 15th and 16th century and as far I know his history from what I found about it, there could be no reason for him to be famous in the Liege area : 1) he served mostly in Italy and South of France, apparently not in today�s eastern Belgium or close to Liege and 2) he served France as the Liege area, as well as other vast territories of today�s Wallony (it goes to the west up to the actuel French border), was not a French territory but a Principality under the authority of Liege�s bishop, linked to the Holy Roman Empire of the German Nation . Founded in 985, it remained a confederate state of the Empire up to 1789. For that reason, I doubt the people from Liege and around cared about what Pierre Taillard de Bayard did in Italy for the king of France. The strongest French influence in our area was probably the one of Emperor Napoleon the 1st. In addition, Pierre de Bayard fought Emperor Karl V (Also an historical figure ni Belgium), and was thus an ennemy of the Liege principality as it was a part of th� Holy Roman Empire.
My 2 cents, history is not my specialty.
Interesting fact is that Saint Hubert, which his legend is one the most famous hunting legend among European hunters (you know, the white stag appearing to him with a shining christian cross between the racks showing that the heavenly lord was wanting the noble people go to the church instead of hunting all the time �), was the first historical character to play a major role in the founding of Liege as a major city and a principality.