Photometric time series of the gamma Doradus star 43 Cyg obtained with the BRITE-Constellation nano-satellites allow us to study its pulsational properties in detail and to constrain its interior structure. We aim to find a g-mode period spacing pattern that allows us to determine the near-core rotation rate of 43 Cyg and redetermine the star's fundamental atmospheric parameters and chemical composition. We conducted a frequency analysis using the 156-days long data set obtained with the BRITE-Toronto satellite and employed a suite of MESA/GYRE models to derive the mode identification, asymptotic period spacing and near-core rotation rate. We also used high-resolution, high signal-to-noise ratio spectroscopic data obtained at the 1.2m Mercator telescope with the HERMES spectrograph to redetermine the fundamental atmospheric parameters and chemical composition of 43 Cyg using the software Spectroscopy Made Easy (SME). We detected 43 intrinsic pulsation frequencies and identified 18 of them to be part of a period spacing pattern consisting of prograde dipole modes with an asymptotic period spacing of 2970(+700,-570)s. The near-core rotation rate was determined to be 0.56(+0.12,-0.14)c/d. The atmosphere of 43 Cyg shows solar chemical composition at an effective temperature of 7150+/-150K, a logg of 4.2+/-0.6dex and a projected rotational velocity, vsini, of 44+/-4km/s. The morphology of the observed period spacing patterns shows indications of the presence of a significant chemical gradient in the stellar interior.