We present the data of the Plateau de Bure Arcsecond Whirlpool Survey ( PAWS ) , a high spatial and spectral resolution ^ { 12 } CO ( 1–0 ) line survey of the inner \sim 10 \times 6 \mathrm { 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 \mathrm { pc } ) . We describe the observation , reduction , and combination of the Plateau de Bure Interferometer ( PdBI ) and IRAM-30m ‘ ‘ short spacing ’ ’ data . The final data cube attains 1.1 \arcsec -resolution over the \sim 270 \arcsec \times 170 \arcsec field of view , with sensitivity to all spatial scales from the combination of PdBI and IRAM-30m data , and brightness sensitivity of 0.4 \mathrm { K } ( 1 \sigma ) in each 5 \mathrm { km s ^ { -1 } } -wide channel map . We find a CO-luminosity of 9 \times 10 ^ { 8 } \mathrm { K km s ^ { -1 } pc ^ { 2 } } , corresponding to a molecular gas mass of 4 \times 10 ^ { 9 } \mathrm { M _ { \odot } } for a standard CO-to-H _ { 2 } conversion factor . Unexpectedly , we find that a large fraction , ( 50 \pm 10 ) \% , of this emission arises mostly from spatial scales larger than 36 \arcsec \simeq 1.3 \mathrm { 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 \mbox { $ { } ^ { 12 } $CO } / \mbox { $ { } ^ { 13 } $CO } ratio , and the difference between the kinematics and structure of the PdBI-only and hybrid synthesis ( PdBI + IRAM-30m ) images . The extended emission is consistent with a thick , diffuse disk of molecular gas with a typical scale height of \sim 200 \mathrm { pc } , substructured in unresolved filaments which fills \sim 0.1 \% of the volume .