The spectrum of the Sun matches the spectrum of elements.
Only if the Sun is strictly gaseous, spectroscopy's fun like that. An illuminated solid body emits a continuous spectrum, no matter the material it's made from; that's how we can use spectroscopy to determine the elements around such an object by looking at the emission lines without spending a whole other paper trying to work out what the light source is composed of. For a gaseous light source the gas composing it creates emission spectra, for a solid light source the gas
surrounding it gives the spectra. The spectrum of the Sun can't be used to argue that it's composed of those elements unless you've demonstrated it has to be wholly gaseous. A FEer could just reply that it is a solid body and those elements are just present at some point between the Sun and us.
Offhand I couldn't tell you precise mechanisms for illumination under generic FE models, though that's mostly because the atypical models are more memorable for me. Davis's non-Euclidean model allows for a Sun of the same composition and size with gravity, JRowe's relies on friction thanks to an interesting mdoel of space, Sandokhan's is based on fundamentally different physics...