Neutron scattering experiments have been performed on the ternary rare-earth diborocarbide Ce$^{11}$B$_2$C$_2$. The powder diffraction experiment confirms formation of a long-range magnetic order at $T_{rm N} = 7.3$ K, where a sinusoidally modulated structure is realized with the modulation vector ${bm q} = [0.167(3), 0.167(3), 0.114(3)]$. Inelastic excitation spectra in the paramagnetic phase comprise significantly broad quasielastic and inelastic peaks centered at $hbar omega approx 0, 8$ and 65 meV. Crystalline-electric-field (CEF) analysis satisfactorily reproduces the observed spectra, confirming their CEF origin. The broadness of the quasielastic peak indicates strong spin fluctuations due to coupling between localized $4f$ spins and conduction electrons in the paramagnetic phase. A prominent feature is suppression of the quasielastic fluctuations, and concomitant growth of a sharp inelastic peak in a low energy region below $T_{rm N}$. This suggests dissociation of the conduction and localized $4f$ electrons on ordering, and contrasts the presently observed incommensurate phase with spin-density-wave order frequently seen in heavy fermion compounds, such as Ce(Ru$_{1-x}$La$_x$)$_2$Si$_2$.
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