  For several years, the metastable helium triplet line has been successfully
used as a tracer to probe atmospheric escape in transiting exoplanets. This
absorption in the near-infrared (1083.3 nm) can be observed from the ground
using high-resolution spectroscopy, providing new constraints on the mass-loss
rate and the temperature characterizing the upper atmosphere of close-in
exoplanets.
  The aim of this work is to search for the He triplet signature in 15
transiting exoplanets -- ranging from super-Earths to ultrahot Jupiters --
observed with SPIRou, a high-resolution (R~70 000) near-infrared
spectropolarimeter at the CFHT, in order to bring new constraints or to improve
existing ones regarding atmospheric escape through a homogeneous study.
  We developed a full data processing and analysis pipeline to correct for the
residual telluric and stellar contributions. We then used two different 1D
models based on the Parker-wind equations and nonlocal thermodynamic
equilibrium (NLTE) radiative transfer to interpret the observational results.
  We confirm published He triplet detections for HAT-P-11 b, HD 189733 b, and
WASP-69 b. We tentatively detect the signature of escaping He in HD 209458 b,
GJ 3470 b, and WASP-76 b. We report new constraints on the mass-loss rate and
temperature for our three detections and set upper limits for the tentative and
nondetections. We notably report improved constraints on the mass-loss rate and
temperature of the escaping gas for TOI-1807 b, and report a nondetection for
the debated atmospheric escape in GJ 1214 b. We also conducted the first search
for the He signature in GJ 486 b since its discovery and report a nondetection
of the He triplet. Finally, we studied the impact of important model
assumptions on our retrieved parameters, notably the limitations of 1D models
and the influence of the H/He ratio on the derived constraints.
