Franklin, the sole Black member of the Peanuts ensemble, is sitting all by himself on one side of the table.
The scene in question is, in fact, somewhat questionable itself: the numbers of chairs and servings fluctuate throughout, giving the meal a disorientating Kubrickian quality. This produces in the scene a sense of unease and tension which reflects the viewers’ discomfort at the casual racism on display. Indeed, Franklin is seated in the malicious beach chair, which humiliatingly places him at an eye level below that of the others.
Though this segregation is not limited to racial issues only: Marcie, though eccentric and possessing of an ambiguous sexuality, is caucasian enough to be allowed to remain close to the rest, but is still seated at the end towards the left side of the table. Linus chooses to seat Marcie as far away from himself as possible, separated from the larger group by the dog. Indeed, the beagle is deemed a more fit companion than any heterodox humans. (Though, perhaps Snoopy is allowed to sit with the elite in due respect for his cooking prowess. It is also noted that Snoopy, in an act of defiant compassion, serves Marcie and Franklin first.) Furthermore, to extrapolate, the only characters exempted which could reasonably join the table next are the obsessive-compulsive Schroeder, the filthy Pig Pen, or the unloved and sadistic Lucy, who, if arriving late, would be forced to sit in one of the chairs next to Franklin and Marcie. Thus, the entire left side of the table would be relegated to odd, unhygienic misfits and belligerent, racial outcasts.
The characters are not evil: Peppermint Patty shows genuine remorse for embarrassing and bullying Charlie Brown, and Linus is often a beacon of compassion and temperance. But the point is made: the virus of casual discrimination is insidious and unaware, and can manifest itself at an early age.
Source: The Journal of Carton Overanalzations
Franklin ©  Peanuts Worldwide LLC