The level mixing spectroscopy method has been applied to measure the static quadrupole moments of six isomeric states in Fr-213, Fr-212, and Fr-211 (Z = 87). For isomers with the proton configuration pi-h9(4)/2i13/2 a large increase of the quadrupole moment was observed with the removal of neutrons from the closed N = 126 core: Q(29/2+,Fr-213) = -70(7) e fm2, Q(15-,Fr-212) = -80(12) e fm2, and Q(29/2+,Fr-211) = -107(18) e fm2. Quadrupole moments for very high spin states were also measured: Q(65/2-,Fr-213) = -219(53) e fm2, Q(27-,Fr-212) = -152(31) e fm2, and Q(45/2-,Fr-211) = -198(56) e fm2. The observed values are in good agreement with shell-model calculations, but are lower than that predicted using the deformed-independent particle model. The implantation behavior of Fr in a Tl host is also discussed.