Cruncher helps convince Barsad to cooperate with Carton because he can tell the French that Barsad is a spy.
Sydney Carton wants to do anything he can to help the Manettes and Darnay. With Jerry Cruncher, they establish that Barsad is a spy. Jerry Cruncher shares that he knows that they buried bricks in Roger Cly’s coffin, and he can denounce Barsad as a spy at any time. Barsad’s association with Cly can be shown.
I hold another card, Mr. Barsad. Impossible, here in raging Paris, with suspicion filling the air, for you to outlive denunciation, when you are in communication with another aristocratic spy of the same antecedents as yourself, who, moreover, has the mystery about him of having feigned death and come to life again! (Book 3, Ch 8)
Sydney Carton’s “card game” is his attempt to convince Barsad to cooperate with him. Carton has a plan, and now he can force Barsad to go along with it. It is very important to Carton to save Darnay, because the love of his life is married to him.