You can absolutely integrate your booking form with your Facebook Page. You can start by clicking on the "Page Button" option it will open this dialog:
Then choose the "Book with you" option, then choose "Book Now"
Click on "Next" and choose the "Link to website" option:
And then enter the URL of your booking form.
To obtain the URL of your booking form, you need to go under the "Online Booking" page. You can click on the eye button (next to the share button against the booking form):
You can then copy the link (URL) from the search bar of your browser:
This is the link you need to paste on your Facebook Page.