Before you install the pre-hung French doors in the newly enlarged rough opening, you should finish up doing any electrical work and hang drywall around the sides of the new opening.
Connect the old wiring to any new wiring at a junction box (according to building code, the junction box must remain exposed).
Depending on where the old studs were placed in the pre-existing wall, you may need to install a few new studs or horizontal nailers in spots where you need more solid backing to nail up drywall.
If the French doors are leading outside, you need to insulate the wall in which the doors are placed. Remember: the vapor barrier of any insulation, faced or unfaced, should face the living area. You can use faced insulation by simply installing rolls of it into the wall cavities and stapling it to inside of the studs with the paper facing into the room.
Or, if you don't want to use faced insulation (it's slightly more expensive), you can install a polyethylene vapor barrier over the wall as shown in the image and fill the stud cavities with unfaced insulation.
With either type of insulation be sure to wear a mask and gloves to install.
Measure and cut pieces of drywall. Using drywall screws, lay up the first piece of drywall, apply drywall mesh over cracks, add a first layer of joint compound and smooth out the seams. A fan will help the joint compound dry faster. You'll come back to do finish coats after you hang the doors.
Before installing the French Doors frame, check the sill plate for any deformities, nails or obstructions. Apply three beads of 100-percent non-hardening silicone (don't use constructive adhesive) onto the sill plate to help keep the weather out.
Before installing, caulk behind the nail fins of the doorframe to help create a weather-tight seal.
Set the frame into place. In order for the doors to open and close properly, you'll need to make little adjustments up and down the sides and across the top. You can use just two nails, one in each corner, to hold the frame in place while you do this (Image 1).
With the frame held in place, begin to insert shims (Image 2) along the sides and across the top, looking to get an even space around the doors and the frame -- called the "reveal" (Image 3).
Check the level, plumb and the square of the doorframe (measure corner to corner in both directions -- the two distances should be even) before you complete the installation of the frame. This will help avoid having to come back to make adjustments to the actual door panels themselves. Nothing screams "out of plumb" like a new pair of badly hung French doors.
Once the doors are working properly, nail the fins to the wall, with nails every six to eight inches. Open and close the doors several times while you work your way around the edges, just to make sure the doorframe hangs perfectly.
Once the doorframe is secure in its final position, add a second layer of drywall to match the wall thickness (if needed) or apply a second coat of compound along joints. If it's in the direct vicinity of the door trim, you'll want to finish all drywall taping and sanding before you install the trim.
Pre-prime the door trim. When dry, nail up the door trim on both sides of the doors, using finish nailer and finish nails.
Spackle the nail holes and finish with paint.