There are two single crystal-structure investigations done at room temperature, both published in 1963. Both suggest that $\ce{XeF4}$ crystallizes in monoclinic system ($P 1 2_1/n 1$) and preserves square-planar geometry in solid phase; however, the angle $\ce{F-Xe-F}$ slightly deviates from $90°$.

Figure 1. Packing of $\ce{XeF4}$ molecules. Color code: $\color{#90E050}{\Large\bullet}~\ce{F}$;$\color{#429EB0}{\Large\bullet}~\ce{Xe}$.
Ibers and Hamilton [1] published a structure with an $R$-factor of $11\%$ (ICSD #27467)
The molecule has symmetry $D_\mathrm{4h}$ within the limits of error of this study, although such symmetry is not required by the space group. The angle $\ce{F1-Xe-F2}$ is $\pu{86 ± 30°}$ and the two independent distances $\ce{Xe}$ to $\ce{F}$ do not differ significantly and have an average value of $\pu{1.92 ± 0.03 Å}$ (Fig. 1). The shortest intermolecular $\ce{F...F}$ contact is $\pu{2.95 Å}$. This and all other intermolecular distances are reasonable; the molecule fills space well, providing further confirmation of the formula $\ce{XeF4}$. Since all of the intermolecular $\ce{F...F}$ contacts in this structure exceed slightly the expected van der Waals contact of $\pu{2.7 Å}$ it is not surprising that a second phase of $\ce{XeF4}$, with a density some $10$ percent higher than that of the present structure, exists (2). The structure of this denser phase is at present unknown.

Fig. 1. The structure of the $\ce{XeF4}$ molecule in the solid.
Templeton et al. [2] did a subsequent XRD experiment and presented improved crystallographic data (ICSD #26626) with $R$-factor of $8.6\%$ and stated that
The structure consists of a molecular packing of square planar molecules of $\ce{XeF4}$.
With a comment on [1]:
Ibers and Hamilton have deduced two structures by refinement of data with $h + k + l$ even. These data do not permit determination of the relative signs of the two $y$ coordinates. One of these two structures is in approximate agreement with our result.
References
- Ibers, J. A.; Hamilton, W. C. Xenon Tetrafluoride: Crystal Structure. Science 1963, 139 (3550), 106–107. https://doi.org/10.1126/science.139.3550.106.
- Templeton, D. H.; Zalkin, A.; Forrester, J. D.; Williamson, S. M. Crystal and Molecular Structure of Xenon Tetrafluoride. Journal of the American Chemical Society 1963, 85 (2), 242–242. https://doi.org/10.1021/ja00885a038.