Spread generous amount over one side of two slices French bread. Assemble sandwich with chicken strips, 1 tablespoon pasta sauce, sprinkling of Parmesan cheese, and one slice mozzarella cheese.
Top with second slice of French bread.
Repeat for remaining sandwiches.
Grill sandwiches on tabletop grill or griddle for 4-5 minutes on each side, flipping if you don't have a two sided grill.
Allow sandwiches to sit for 5 minutes before slicing.