Velcro has a limited life when regularly exposed to water and gunk. A good example are the shoes with Velcro straps for the top closure. The Velcro wears out fairly soon.
You can buy very light weight snaps in notions sections of sewing and department stores. As stated, they come in plastic, as well as metal.
They are easy to mount with a the little hammer and anvils that come with them, once you get the hang of it.
Get ones just heavy enough to have a good grip that won't pop open with the slightest pressure.
If you really wanted a pull-proof closure, you could use kitty clips, or tiny plastic rings and mitten hooks; but it would make it take longer to install the floor with each pitch, and that amount of holding power may not be necessary.
I have used snaps, one every foot or so, on small tarp floors for tarp tents, and it worked fine - no failures, even with winter camping in the snow. I think it is because if the tarp or tarp tent is well and securely pitched, there is no great pressure on the tarp-to-floor connecting snaps. What the snaps do is keep the sides of the floor lifted up and connected to the top tarp, several inches above the ground, so rainwater can't flow in. To survive wear and tear, small reinforcement fabric patches should be bonded to the top and bottom tarps at the point where each snap is installed.