First cut the top off a 1-liter plastic bottle. This will act as an insert to hold water and the flowers.

Fold the placemat around the bottle to ensure a snug fit. 

Use a safety pin to hold it in place. It will be on the back where no one will see it. You could try hot glue if you don't like the idea of a safety pin.

Add grommets at the top of the placemat, one on each side to hold the wire.

Feed the wire through the grommets and twist the ends back on themselves to create a secure hanger.

Add water to the plastic bottle, about 2/3 full.

Place it in the burlap vase and hang.

Arrange flowers inside and enjoy.