Micro-joule UV-range (350-415 nm) femtosecond-laser pulses generated via frequency-doubled parametric conversion of 525-nm 150-fs pulses of Yb-glass laser were used for "hot" photoluminescence excitation in a diamond plate enriched by blue-emitting N3-centers (zero-phonon line, ZPL, at 415 nm). Photoluminescence spectra acquired in the range of 400-500 nm exhibited wavelength-independent well-resolved ZPL and phonon progression bands, where the involved phonons possessed the only energies of 0.09 eV (LA-phonons) and 0.15 eV (softened LO/TO-phonons), potentially, as a result of a Clemens decay mechanism. Photoluminescence yield in the ZPL and other phonon bands exhibited the power slope of 1.8 at lower energies and ≈1 at higher energies. The transition zone at fluence ∼1014-15 photons/cm2 was related to the saturation of the pumped resonance transition and the slower non-radiative vibrational relaxation to the ZPL-related excited electronic state and the nanosecond spontaneous photoluminescence transition to the ground state. As a result, the absorption cross section σ(370-390 nm) ≈1·10-15 cm2 and concentration [N3] ≈6·1014 cm-3 were determined along with the ZPL absorption cross section σ(415 nm) ≈2.5·10-15 cm2, and the non-radiative vibrational relaxation rate was estimated, providing altogether the crucial information on lasing possibilities in N3-doped diamonds.