Some runaway stars are known to display IR arc-like structures around them, resulting from their interaction with surrounding interstellar material. The properties of these features as well as the processes involved in their formation are still poorly understood. We aim at understanding the physical mechanisms that shapes the dust arc observed near the runaway O star AEAur (HD34078). We obtained and analyzed a high spatial resolution map of the CO(1-0) emission that is centered on HD34078, and that combines data from both the IRAM interferometer and 30m single-dish antenna. The line of sight towards HD34078 intersects the outer part of one of the detected globulettes, which accounts for both the properties of diffuse UV light observed in the field and the numerous molecular absorption lines detected in HD34078's spectra, including those from highly excited H2 . Their modeled distance from the star is compatible with the fact that they lie on the 3D paraboloid which fits the arc detected in the 24 {\mu}m Spitzer image. Four other compact CO globulettes are detected in the mapped area. These globulettes have a high density and linewidth, and are strongly pressure-confined or transient. The good spatial correlation between the CO globulettes and the IR arc suggests that they result from the interaction of the radiation and wind emitted by HD 34078 with the ambient gas. However, the details of this interaction remain unclear. A wind mass loss rate significantly larger than the value inferred from UV lines is favored by the large IR arc size, but does not easily explain the low velocity of the CO globulettes. The effect of radiation pressure on dust grains also meets several issues in explaining the observations. Further observational and theoretical work is needed to fully elucidate the processes shaping the gas and dust in bow shocks around runaway O stars. (Abridged)< Réduire