  Photometric time series of the $\gamma$ Dor 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 $\Delta
\Pi_{l=1}$ of $2970^{+700}_{-570} \rm s$. The near-core rotation rate was
determined to be $f_{\rm rot} = 0.56^{+0.12}_{-0.14}\,\rm d^{-1}$. The
atmosphere of 43 Cyg shows solar chemical composition at an effective
temperature of 7150 $\pm$ 150 K, a log g of 4.2 $\pm$ 0.6 dex and a projected
rotational velocity, $v {\rm sin}i$, of 44 $\pm$ 4 kms$^{-1}$. The morphology
of the observed period spacing patterns shows indications of the presence of a
significant chemical gradient in the stellar interior.
