I am sure there are many ways to do this, but here are a few suggestions. The options depend to some extent on what equipment you have. For starters, the next time you have a similar project you might consider cutting a tenon on the rails and a mortise in the leg, and glue the stile to the leg directly. If the weight of the piece is transferred to the floor through that joint, there will be a moment of force on that area and the joinery there has to be good.
For this one, it appears that the rails (the horizontal piece at the top and bottom) go across the top of the stiles (the side pieces). I will refer to that terminology to make my explanation clear. You can put a floating tenon for the rail to leg joint then and simply glue the legs to the styles. Thatís a long grain to long grain joint and if done correctly it should be stronger than the wood itself. You could even omit the floating tenon in the rails and rely on the long grain to long grain joint, though there might be some wobble where the rail touches the leg if the piece is moved or treated roughly.
If you have one, a biscuit joint could be used to align the rail to leg joint and to align the stiles to the leg, but donít rely on it alone. It may not be strong enough to carry the weight of the piece, but could work depending on what you plan on using the furniture for. Finally, you can use a spline by cutting a matching groove in the legs and the face frame.
Additionally, while there are no correct designs, many traditional frames are made with the styles going from top to bottom, and the rails fitting between them, though there are thousands of exceptions. With that taken into consideration, you could eliminate the face frame assembly, and secure the rails directly to the legs via mortise and tenon, though I think your design looks good as it is. It looks like a nicely executed and designed project. Good luck with it.