139La NMR and relaxation measurements have been performed on La{1.8-x}Eu{0.2}Sr{x}CuO{4} (x = 0.13 and 0.2) single crystals. The temperature dependence of the 139La NMR spectra in all the structural phases (HTT -> LTO -> LTT) reveals the non-vanishing tilt angle of the CuO6 octahedra in the HTT phase, opposed to the case of La{2-x}Sr{x}CuO{4} where the tilt angle disappears immediately above the transition. Since 139La relaxation data provide evidence of the thermodynamic critical fluctuations associated with the structural phase transitions, HTT -> LTO and LTO -> LTT, we conclude that the structural transitions in Eu-doped La{2-x}Sr{x}CuO{4} should be of the order-disorder type rather than of the displacive type observed in La{2-x}Sr{x}CuO{4}. The change of the nature of the structural transitions caused by doping Eu appears to be consistent with the LTO -> LTT transition that is absent in La{2-x}Sr{x}CuO{4}. ; Comment: 5 pages, 4 figures, published in PRB