Using small-angle neutron scattering, we have studied the flux-line lattice (FLL) in the superclean, high-kappa superconductor CeCoIn5. The FLL undergoes a first-order symmetry and reorientation transition at approximately 0.55 T at 50 mK. In addition, the FLL form factor in this material is found to be independent of the applied magnetic field, in striking contrast to the exponential decrease usually observed in superconductors. This result is consistent with a strongly field-dependent coherence length, proportional to the vortex separation.