We present the data of the Plateau de Bure Arcsecond Whirlpool Survey, a high spatial and spectral resolution 12 CO (1-0) line survey of the inner ∼10 × 6 kpc of the M51 system, and the first wide-field imaging of molecular gas in a star-forming spiral galaxy with resolution matched to the typical size of giant molecular clouds (40 pc). We describe the observation, reduction, and combination of the Plateau de Bure Interferometer (PdBI) and IRAM-30 m "short spacing" data. The final data cube attains 1. 1 resolution over the ∼270 × 170 field of view, with sensitivity to all spatial scales from the combination of PdBI and IRAM-30 m data, and a brightness sensitivity of 0.4 K (1σ ) in each 5 km s −1 -wide channel map. We find a CO luminosity of 9 × 10 8 K km s −1 pc 2 , corresponding to a molecular gas mass of 4 × 10 9 M for a standard CO-to-H 2 conversion factor. Unexpectedly, we find that a large fraction of this emission, (50 ± 10)%, arises mostly from spatial scales larger than 36 1.3 kpc. Through a series of tests, we demonstrate that this extended emission does not result from a processing artifact. We discuss its origin in light of the stellar component, the 12 CO/ 13 CO ratio, and the difference between the kinematics and structure of the PdBI-only and hybrid synthesis (PdBI + IRAM-30 m) images. The extended emission is consistent with a thick, diffuse disk of molecular gas with a typical scale height of ∼200 pc, substructured in unresolved filaments that fill ∼0.1% of the volume.