FBQS J1644+2619 is one of the most recently discovered $\gamma$-ray emitting Narrow-Line Seyfert 1s (NLSy1s). Here we present a multiwavelength analysis of this source, focussing on a recent 80 ks X-ray observation with XMM-Newton. The spectral energy distribution of the source is similar to the other $\gamma$-ray NLSy1s, confirming its blazar-like nature. The X-ray spectrum is characterised by a hard photon index ($\Gamma = 1.66$) above 2 keV and a soft excess at lower energies. The hard photon index provides clear evidence that inverse Compton emission from the jet dominates the spectrum, while the soft excess can be explained by a contribution from the underlying Seyfert emission. This contribution can be fitted by reflection of emission from the base of the jet, as well as by Comptonisation in a warm, optically thick corona. We also compare these results with X-ray observations of other $\gamma$-ray NLSy1s. The majority of the sources have similar X-ray spectra, with properties intermediate between blazars and radio-quiet NLSy1s.