Paper has the habit of becoming wavy when wet with water (other liquids too).
So the first thing you might want to try is ti use a non-watery glue, but still suitable for paper.
For the next projects, you might want to investigate about the types of paper available, to choose one more suitable for what you intend to do.
During curing, make sure to apply pressure to the area with the glue - on a flat surface, of course. Worst case, turn a kitchen table up-side-down, place it over the collage, and then add some serious weight over (now inside) it. The floor has to be flat also, or use another table as a support.
Another hint: use a non-stretchable support for the collage, e.g. glass-fiber mesh. You can even build a sandwich: cardboard + glass-fiber mesh + collage (for some added strength).