The red circle, according to Buddha and the film's epigram, is where everyone who is destined to meet each other will finally meet. In the film, we are introduced to various men at certain arcs of their trajectory towards that circle.
The day before his release from prison, Corey (Alain Delon) is given a tip by a guard on a job once he's out. Corey goes to Rico, his old partner who has repaid his loyalty by stealing his woman. In return, Corey helps himself to the money in Rico's safe. Which obligates Rico to send some thugs after him. One thing always leads to another.
Meanwhile, Vogel (Gian Maria Volonté), the perpetrator of some unknown crime, escapes from custody and hides in the trunk of Corey's car. Corey provides Vogel's freedom and Vogel returns the favor by killing Rico's thugs. They win each other's trust the only way criminals can, by further implicating themselves in crime. It is a single-direction trip that can only gain momentum.
Inspector Matthei (André Bourvil) is the Spencer Tracy look-alike who was supposed to be guarding Vogel when he escaped. He is the Lt. Philip Gerard to Vogel's Fugitive. He is a good guy, but he has to prove himself to the head of Internal Affairs who asserts, "No one is innocent. All men are guilty."
To round out the team implementing the plan leaked to Corey in jail, Vogel recommends Jansen (Yves Montand), an alcoholic ex-cop with demons and issues of his own to work out.
And last there is Santi (François Périer) who is sort of the bridge between crime and punishment, as it were. He's the bar owner/ mob tie that is Matthei's best link to finding Vogel. Like all of the men, he operates by a code, honor among thieves, and won't rat them out. Unless, of course, he does.
Director Jean-Pierre Melville (Bob le Flambeur, Le Samourai) is very good at taking each man at an exact moment somewhere in the middle of their stories and very subtly exposing their entire history.
Coming towards the end of his career, Le Cercle Rouge is supposed to be a culmination of everything Melville has learned from his experiences making crime films. It's his own private red circle, so to speak.
In terms of pacing and mood, it is much more akin to The Asphalt Jungle than The Italian Job. It is not focused on action, but slowly and evocativley building real characters. They may be guilty but they are not amoral. It is each person's sense of duty or honor which propel them to their ineluctable end.