San Francisco, Juno 7. Arrived, tho sfenmHhip Constitution frotn Pannmn, with date via Acíipulec, of thc 18th üf May of Puebla, and 19lh Ironi tho City ol Mexico. On tho 15th aiul 16tb the Mexicans were repulsed before the Fortress Carmen. - Tho garrison and inhabitants oí' Puebla wore in a stuto oí' starvation. Tho ammunilion wae íailifig and Ortega was disappointed that Commonfort could not out his way through with supplies f'orthe besieged. On ti.e 17th Oen eral, Forcy sent a iag of truoe offering to allow the Mexioan oílicers and soldiers to march out, the officers with sido arma, providing thcy givo parolo not to serve against tho Frenob. This was declinod by Ortega, who, n tlie mean ti me, spiked the cannon, burned the gun cnrriages, destroyed the iní'antry arras, and thon surrendored. - Tho Síexican General Reguíos, and his aida and hia ordnance officers, preferring death to being prisoners, shot themsolves defd, The advanco of the FrcDch army was nt Cholula, twontyfour triles beyoud Puebla; on its way to tho capital. The Jlexicans veere muoh embittered against the Frcnch. and all Frcnch men ero ordored to loavo the capital within eight days. The Mexicans will defend tho approachos to tho capital to tho last, Greflt ontliuiia.sm revails. This account is from Medican sources. In San Francisco tho Mexican housts aro drnped, while from tho French houses llaga uro ílying.