I did something similar the first time I made this pattern.
I had to sew the skirt side seams in layers; the base fabric was french seamed, the overlay was french seamed, and then I put the 2 layers of skirt together before attaching to the bodice. For the bodice, I basted and then sewed the side seams wrong side together, ironed (I have an iron cover to protects the fabrics from the direct iron heat, if you don’t, use an ironing cloth) until the seam was good and set, trimmed the seam bulk, turned, ironed again, and finally stitched the rest of the french seam. Once the seam was sewn, I ironed it again to set the seam, and before it could cool, I turned the bodice right side out and ironed the seam again, making sure the fabric layers were smooth and neat.
I hope this helps.