Applying the CW laser absorption and fluorescence method, the cross sections for the fine structure mixing and quenching of the Cs(6P) state, induced by collision with N2 molecules, were measured. Cesium atoms were optically excited to the 6P3/2 state. The excited atom density and spatial distribution were mapped by monitoring the absorption of a counterpropagating single mode laser beam, tuned to the 6P1 --> 8S(1/2) transitions, which could be translated parallel to the pump beam. The transmission factors, which describe the average probability that photons emitted within the fluorescence detection region can pass through the optically thick vapor without being absorbed, were calculated for 6P --> 6S(1/2) transitions. The N2 caused line broadening and therefore increased the effective pumping rate and radiative rates. The effective radiative rates were calculated for the 6P(J) --> 6S transitions. The fluorescence intensity I895 of the sensitized 6P(1/2) --> 6S(1/2) emission was measured as a function of N2 density in the range 2 x 10(16) < N < 1.4 x 10(17) cm(-3) at a constant temperature T = 337 K, which produced cesium density N0 = 1.25 x 10(12) cm(-3). The transparency of the cell was obtained by the absorption of light beam passing the cell. The transparency is not a simple function of N2 density. It was found that the quantity N/I895 (I895 being corrected for the cell transparency) exhibited a parabolic dependence on N, confirming that the quenching of the 6P(J) states is due to collision with N2 molecules instead of Cs ground state atoms. The coefficients of the second-order polynomial fitted through the measured data yielded the cross sections sigma3/2 --> 1/2 = (0.42 +/- 0.17) x 10(-16) cm2 and sigmaD = (1.31 +/- 0.52) x 10(-16) cm2 for the 6P(J) fine-structure mixing and quenching, respectively, due to collision with N2 molecules. The quenching rate coefficient is about 3 times larger than the rate coefficient for the fine-structure mixing. Our values for these cross sections are in agreement, within combined error bars, with the values we have recently obtained under different experimental conditions.