Context. The flat-spectrum radio quasar 4C +71.07 is a high-redshift (z = 2.172), γ-loud blazar whose optical emission is dominated by thermal radiation from the accretion disc. Aims: 4C +71.07 has been detected in outburst twice by the AGILE γ-ray satellite during the period from the end of October to mid-November 2015, when it reached a γ-ray flux of the order of F(E > 100 MeV)=(1.2 ± 0.3)×10-6 photons cm-2 s-1 and F(E > 100 MeV)=(3.1 ± 0.6)×10-6 photons cm-2 s-1, respectively, allowing us to investigate the properties of the jet and the emission region. Methods: We investigated its spectral energy distribution by means of almost-simultaneous observations covering the cm, mm, near-infrared, optical, ultraviolet, X-ray, and γ-ray energy bands obtained by the GASP-WEBT Consortium and the Swift, AGILE, and Fermi satellites. Results: The spectral energy distribution of the second γ-ray flare (whose energy coverage is more dense) can be modelled by means of a one-zone leptonic model, yielding a total jet power of about 4 × 1047 erg s-1. Conclusions: During the most prominent γ-ray flaring period our model is consistent with a dissipation region within the broad-line region. Moreover, this class of high-redshift, flat-spectrum radio quasars with high-mass black holes might be good targets for future γ-ray satellites such as e-ASTROGAM. Partly based on data taken and assembled by the WEBT collaboration and stored in the WEBT archive at the Osservatorio Astrofisico di Torino - INAF (http://www.oato.inaf.it/blazars/webt).