Washington, May 5. The State Department has furniehed tho presa the offuial correspondente botween Ministers Faulkner and 'J'nouvo nol on American affaire, Faulkner informed him : 'J'hat tho Président cntertaincd ;i full cocfideoce oí tbe speedy restoratiou of the hartnony and unity oí' the governmoiit ; That eventa might produce a tcmporary inoonvonienee to French snbjeels, bat, all injury sboild be iodemnified ; That thu President thought it not itnprobable that there would be an appeul made to foreign governn:ents by tho Confedérate States for reuognition of thuir independence, and, when sucb appenl was made, it will be opposed by the Minia er wbo muy thcn represent, iho United States. Faulkner said that the ouly request ho liad '.o make was, that no propositio:i recognizipg the dismeruberrnent oí the CJoioa sha) I be oonsiderad by France til! the arrival ot the new fthñister, who will be iully instructud. Thouvenel replied that no applioation had yet been made; that the French govarninent never acted bastily on such questioos ; and he as.-ured Faulkmr ihat no precipítate aotion would be taken on tbe s-ub;eet by the Eniperor. JIo said the establiebed usage was to recognize a de fatto goveronient wheo i proper case was made out In reply to a questioo, Faulkner said be thought that force would not bo used. The only solution was am dification of the cooetitutioD, or a peaceable aequieecence in the claim to separate eovereigaty. Thouvenel thought the employment of force uuvvise. In the Socretary of State's instrucrions to Minister Dayton, he is to oonsider instruotionu to the former Minister by the President as ucohangeable. ■Notwithstanding any opinión expressed or recordud by bis predecèssor, he is to assure Thouvenel that no difiereooe of opinión exists bet ween t'ne President und his Cabintt. Tho piith is plainly marked out by stern necof.-.ity, and not by the hands ol' tiiis admioistration is tiiis government to end. Franoe's assurance not to take any hasly steps is considered eatisfuctory, although uLtendud by reservaiions. öeward says, in reply to Fuulkner's answer, that foroe wonld not bo used, &c , th.it the time wben these quostiona bad ütiy pertinenoy has paesed. Insurgente, with deadly war, tried to compel tho government to recognize the dismemberment of the Union. We bave accepted thia civil wor as inevitable of oecesaity. Oonsthutional remedies are stil! open to the insurgonts, and will remaio so. You cannot Da too decided in making known to the French govei nraent that no idea does, or wil!, exist of suffering a diasol ution of the Union to take place in any way, peaceably or foroibly. It has" oever entered the niiod cf any candid statesman here, and ii is high timo lo be disraissed by E uro pean statcsnien.