A fluidic connection device for a fluid circuit, in particular of a vehicle, this device comprising: - a first pipe comprising a main section of internal diameter D1 and a secondary section having at least one internal diameter D2 greater than D1, the secondary section being located at one end of the first pipe and connected to the main section by a first shrinkage, this first pipe being made of a plastically deformable material and comprising a first external annular collar, - a tubular end-piece comprising an end section of external diameter D3 which is configured to be engaged along an axis A in the secondary section of the first pipe, this end-piece comprising an external cylindrical shoulder, - a first flange mounted around the secondary section of the first pipe and comprising a first orifice crossed by this secondary section, this first flange being configured to be supported axially on the first collar, - a second flange mounted around the end-piece and comprising a second orifice crossed by this end-piece, this second flange being configured to be supported axially on the cylindrical shoulder of the tubular end-piece, the first and second flanges (16, 18) being configured to be tightened one against the other in a connecting plane substantially perpendicular to said axis A so as to bring the first collar closer to said cylindrical shoulder and to maintain the end-piece engaged in the first pipe, - at least one element for attaching the first and second flanges (16, 18) one against the other, the device being characterized in that it comprises: - a non-return insert valve mounted within said secondary section of the first pipe, and located axially between said first shrinkage of the first pipe and said end section of the tubular end-piece, and in that said secondary section of the first pipe comprises a first segment in which is mounted the end section and which has an internal diameter D2' greater than D1, and a second segment in which is mounted the valve, said second segment being located between the main section and said first segment and having an internal diameter D2 greater than D1 and less than D2'. - a first pipe comprising a main section of internal diameter D1 and a secondary section having at least one internal diameter D2 greater than D1, the secondary section being located at one end of the first pipe and connected to the main section by a first shrinkage, this first pipe being made of a plastically deformable material and comprising a first external annular collar, - a tubular end-piece comprising an end section of external diameter D3 which is configured to be engaged along an axis A in the secondary section of the first pipe, this end-piece comprising an external cylindrical shoulder, - a first flange mounted around the secondary section of the first pipe and comprising a first orifice crossed by this secondary section, this first flange being configured to be supported axially on the first collar, - a second flange mounted around the end-piece and comprising a second orifice crossed by this end-piece, this second flange being configured to be supported axially on the cylindrical shoulder of the tubular end-piece, the first and second flanges (16, 18) being configured to be tightened one against the other in a connecting plane substantially perpendicular to said axis A so as to bring the first collar closer to said cylindrical shoulder and to maintain the end-piece engaged in the first pipe, - at least one element for attaching the first and second flanges (16, 18) one against the other, the device being characterized in that it comprises: - a non-return insert valve mounted within said secondary section of the first pipe, and located axially between said first shrinkage of the first pipe and said end section of the tubular end-piece,