Aims. To investigate the inner regions of protoplanetary disks, we performed near-infrared interferometric observations of the classical T Tauri binary system S CrA. Methods. We present the first VLTI-GRAVITY high spectral resolution (R ∼ 4000) observations of a classical T Tauri binary, S CrA (composed of S CrA N and S CrA S and separated by ∼1 . 4), combining the four 8-m telescopes in dual-field mode. Results. Our observations in the near-infrared K-band continuum reveal a disk around each binary component, with similar half-flux radii of about 0.1 au at d∼130 pc, inclinations (i =28±3• and i =22±6 • ), and position angles (PA=0 • ±6• and PA=-2 • ±12• ), suggesting that they formed from the fragmentation of a common disk. The S CrA N spectrum shows bright He i and Brγ line emission exhibiting inverse P-Cygni profiles, typically associated with infalling gas. The continuum-compensated Brγ line visibilities of S CrA N show the presence of a compact Brγ emitting region the radius of which is about ∼0.06 au, which is twice as big as the truncation radius. This component is mostly tracing a wind. Moreover, a slight radius change between the blue-and red-shifted Brγ line components is marginally detected. Conclusions. The presence of an inverse P-Cygni profile in the He i and Brγ lines, along with the tentative detection of a slightly larger size of the blue-shifted Brγ line component, hint at the simultaneous presence of a wind and magnetospheric accretion in S CrA N.