First of all if there is PL then the material is direct bandgap. indirect bandgap materials do not lumninescent but thermaly lose their energy.
You can find a linear fit to where the PL starts. The point it intersects with the energy axis is approximately the band gap. There are more accurate ways to find the band gap but this is a simple method using the PL which gives reasonable results.
You can check this article entitled "Photoluminescence analysis of p-doped GaAs using the Roosbroeck–Shockley relation". http://dx.doi.org/10.1088/0268-1242/22/10/016
And also the article entitled "Photoluminescence lineshape of ZnO". http://dx.doi.org/10.1063/1.4897383
From PL peak position in near band region, the energy band-gap indirect semiconductor can be determined.If the material has some defects then PL position slightly shifted towards lower energy.
@Watto : You can get transmission spectra then simply do the Tauc Plot .. you will get the band gap of the material. Also from the ondulance of transmission spectra and use Swanepoel formula...(y)
I will need to see the spectra in order to help some more.
As Arindam Mallick suggested using the Tauc plot is a more accurate way.
In short, in both plots (Tauc or PL) if you extrapolate the linear regime of the plot to the energy axis, the point of intersect with the axis gives the band gap energy.