Continuity mistake: During the entire battle the ground is sticky mud. When the French cavalry charge however the ground is dry, so dry there is dust coming from the horses' hooves as they gallop.
Continuity mistake: When Ponsonby is killed by lancers, his horse struggles in the mud. One of the shots shows a dark brown horse's legs getting stuck in the mud. All other shots show a grey horse.
Answer: This is decidedly fiction. The historical Ney already published a boastful proclamation (that Napoleon later said disgusted him), declaring the rule of the Bourbons to be over, before he met with Napoleon (March 15). The scene where Napoleon offered himself to be shot had happened several days earlier, with the 5th regiment of the line, before Napoleon even reached Grenoble. It's an entirely different event from Ney's defection.