Maigret and the Tramp

A vagrant living under a bridge is assaulted at night, knocked hard enough to fracture his skull, and thrown into the River Seine. Two bargemen from barges moored nearby fish him out of the cold water before he drowns and he ends up in the hospital in a coma. Chief Superintendent Maigret is called to the scene. One of the bargemen, whose boat is moored near the ramp coming down the embankment, reports seeing two men coming back from under the bridge and departing in a red sports car. The man's identity card provides a name and place of birth - coincidentally the same town as Madame Maigret's sister resides. For once, Madame is able to participate to some degree and assist her husband in his challenging work. The vagrant was at one time a practicing doctor, but has been living in Paris as a bum for many, many years. Maigret knows the down-and-out community do not normally commit violence against each other. What is hidden in the doctor's past?