Montmartre has been carried after a rather sharp struggle. The tricolour now waves over the Buttes. For some hours I witnessed the fighting to day. I found that early this morning all the important positions of Montmartre had been taken by the two Corps d'Armee of Generals Douai and Ladmirault. The latter General had occupied the station of St. Ouen and the Place of Clichy, and he had advanced to Montmartre by an external movement, keeping for some distance outside the ramparts. At the same time General Douai made a direct movement from inside the city by the Parc de Monceaux. In this manner Montmartre had been almost entirely surrounded. There was a hard contest, but the troops succeeded in entering the Buttes. A large number of the Insurgents were killed in the action, and about 4,000 were made prisoners. The number of cannon and mitrailleuses taken was very considerable, amounting to some hundreds. Belleville is still in the hands of the Insurgents, as are also the Hotel de Ville and the Tuileries. The Red flag was floating on them at half-past 5 o'clock. Severe fighting was going on across the Place de la Concorde between the Insurgents occupying the mansion of the Ministry of Marine, at the corner of the Rue Royale, and the troops on the other side of the river in the Palace of the Corps Legislatif. A gunboat which the Insurgents had under the Pont Royal, close to the Tuileries, was firing constantly. The Insurgents in the Rue de Rivoli and the garden of the Tuileries were using mitrailleuses and rifles, and the troops along the Boulevard at the edge of the Place des Invalides, close to the river, were attacking them with four-pounder guns. Fort Vanves was firing on the Insurgent positions in the neighbourhood of Montrouge and the Faubourg St. Germain, and the Federalists were shelling Vanves from Forts Montrouge and Bicetre. There was musketry skirmishing at various points in the Faubourg St. Germain. The Insurgents occupy houses, from which they keep up a rapid fire to impede the march of General Cissey's troops. Among the prisoners taken to-day many have been recognized as old Reds who were actively engaged in the insurrection of June, 1848. A movement has been ordered which will result in completely shutting in the Insurgents within a circle formed by the whole Army of Paris. The Madeleine is in the hands of the military. Several fires have broken out in the city. Colonel Piquemalle, Chief of the Staff of General Verge, was killed to-day. The following circular despatch was yesterday forwarded to the Prefects of the several Departments. "The tricolour flag waves over the Buttes-Montmartre and the Northern Railway station. These decisive points were carried by the troops of Generals Ladmirault and Clinchant, who captured between 2,000 and 3,000 prisoners. General Douai has taken the Church of the Trinity, and is marching upon the Mairie in the Rue Drouot.