What are the two of the strongest comedic scenes in Cyrano de Bergerac?
This is undoubtedly open to interpretation, but the two strongest comedic scenes in Rostand's Cyrano de Bergerac are the "nose" speech in Act I and the scene between DeGuiche and Cyrano as Roxane and Christian get married in Act III. Each of these scenes demonstrates Cyrano's wit and panache, two things of which he is quite proud.
In the first scene, the rather insipid Valvert offers a mild insult to Cyrano. Cyrano has no respect for those who are weak (plus Valvert is part of a nefarious plan which involves Roxane, the woman Cyrano loves). Though Valvert says nothing about Cyrano's prodigious nose, the cadet chooses to take umbrage as if he did and launches into all the things a real man with a real wit might have said. The humor is Cyrano's dramatic exaggeration of his own greatest flaw; he is self-deprecating (making fun of himself) as well as quick-witted.
You are too simple. Why, you might have said--...
'Tis a rock--a crag--a cape--
A cape? Say rather , a peninsula!
In the second scene, Cyrano disguises himself as a man fallen from another planet, something he can do under cover of darkness. As in the incident with Valvert, Cyrano has no respect for DeGuiche and is trying to protect Roxane. His wordplay here regarding the constellations is equally witty and delightful.
Curious place up there--
Did you know Sirius wore a nightcap? True!
The Little Bear is still too young to bite.
In both cases, Cyrano thinks quickly and demonstrates his quick wit, an obvious disdain for men who of low character, and a desire to protect those he loves. In both cases, the humorous scene is followed by a much more serious incident. After the nose speech, Cyrano stabs Valvert in a duel; after the alien scene, Cyrano and Christian are sent to the front lines of battle.
On a personal note, I have directed this play on a high school stage. While there are many comedic moments, these two scenes got the most laughs, by far. If you had asked for a third, I would have suggested the balcony scene.