Quasiperiodic eruptions (QPEs) are high-amplitude, soft X-ray bursts recurring every few hours, associated with supermassive black holes. Many interpretations for QPEs were proposed since their recent discovery in 2019, including extreme mass ratio inspirals and accretion disk instabilities. But, as of today, their nature still remains debated. We perform the first high-resolution X-ray spectral study of a QPE source using the Reflection Grating Spectrometers' gratings on board XMM-Newton, leveraging nearly 2 Ms of exposure on GSN 069, the first discovered source of this class. We resolve several absorption and emission lines including a strong line pair near the N vii rest-frame energy, resembling the P-Cygni profile. We apply photoionization spectral models and identify the absorption lines as an outflow blueshifted by 1700−2900 km s−1, with a column density of about 1022 cm−2 and an ionization parameter
log
(
ξ
/erg cm s−1) of 3.9−4.6. The emission lines are instead redshifted by up to 2900 km s−1, and likely originate from the same outflow that imprints the absorption features, and covers the full 4π sky from the point of view of GSN 069. The column density and ionization are comparable to the outflows detected in some tidal disruption events, but this outflow is significantly faster and has a strong emission component. The outflow is more highly ionized when the system is in the phase during which QPEs are present, and from the limits, we derive on its location, we conclude that the outflow is connected to the recent complex, transient activity of GSN 069, which began around 2010.