We don't meet Dr. Dupont until the very end of the story, when he is waiting for Adam at the entrance to the hospital. This makes him the one character to appear in both Adam's imagined bike journey (though briefly) and his real experience at the hospital. In fact, the first time Adam explicitly acknowledges that he was not actually biking through New England is in regards to Dr. Dupont. He mentions how he likes to bike around the hospital ground and notes that "Dr. Dupont allows me to do this if I promise not to leave the place" (31.14).
Adam describes Dr. Dupont as "a big man with white hair and a sad black mustache" (31.6). He refers to him several times as "gentle" and "soothing," especially his voice, which he directly contrasts to Brint's ("that other voice in that other room") (31.25).
The most important thing about Dr. Dupont is that he is incredibly kind. He is happy to see Adam when he arrives; he doesn't make Adam feel bad for not taking his medication; and he makes the hospital feel like home. The only other character in this narrative who seems kind is Arnold.