I did the headliner on my 95 Eclipse.
It was an aftermarket headliner material with felt material and thin gray foam backing. I used 3m FOAM spray glue. There is also general 3m spray glue but they must make the foam version for some reason. I got it at Advance auto for around...14 a can if I recall. Home depot used to carry it but I had trouble finding it last time. Took me 2 cans...and my headliner is smaller than yours for sure.

You want good coverage. I used 2 coats and criss crossed the 2nd over the first in the other direction. DON'T try to coat it heavily with 1 coat!! I did in one area and it saturated into the foam and ended up with a flat spot. Luckily it was near the edge so it's not noticable.

Follow directions on the can and you'll be ok. It helps to have 2 people to lay the headliner in place to ensure it's laid down evenly.

BTW...I got the headliner material on sale. The 2 cans of glue cost twice as much as the headliner...