Reconstructing biogeochemical Argo profiles is essential to bridge the severe spatiotemporal coverage gaps between abundant physical observations and scarce biogeochemical data, providing the continuous ocean-state representations required for climate models and global carbon budget analyses. A recent convolutional method for profile reconstruction, PPCon, encodes day-of-year, year, latitude, and longitude through four independently learned multilayer perceptrons. These learned encoders add substantial parameter overhead and may yield sub-optimal spatiotemporal representations for the variables being reconstructed. To address this, we introduce FourierBGC, which replaces PPCon's learned encoders with a fixed Fourier-feature encoding of day-of-year, latitude, and longitude, combined with a lightweight learned projection, cutting encoder parameters by 88 %. By directly embedding periodic annual cycles and smooth spatial continuity into input space, this encoding provides strong multifrequency coordinate representations that facilitate lightweight yet highly expressive spatiotemporal representations. Through a controlled ablation holding PPCon's convolutional backbone fixed, FourierBGC outperforms PPCon on all three reconstructed variables (nitrate, chlorophyll-a, and bbp700), and the Fourier encoding achieves the lowest reconstruction error in every sub-basin and season. Disentangling the sources of error reduction reveals that beyond an optimized training procedure, the Fourier encoding yields a consistent, highly parameter-efficient performance boost across all variables. Furthermore, the learned projection's role exhibits variable- and season-specific behavior tied to upper-ocean physics: it is dispensable on nitrate, essential for capturing the complex profile of chlorophyll-a, and on bbp700 helps under summer stratification while costing accuracy in winter, a pattern consistent with the projection expressing vertical water-column structure only when it is present. Overall, FourierBGC demonstrates that structuring spatiotemporal inputs with explicit frequency priors offers a parameter-efficient strategy for reconstructing sparse geophysical and environmental fields.