How long does it take for black plastic sheeting to kill the grass for making new flower beds?

I've moved to a new house, there is a vegetable garden, grass and trees but not much in the way of flowers. I am going to make new flower beds either side of the fruit garden gate opposite the house. I had some pond liner left over from years ago when I muddled the measurements and bought too much, so I put it on the area to kill the grass. Glyphosate is banned here in France. Does anyone know how long it will take to kill the grass enough for digging?
Dordogne and Norfolk
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Tui
I would suggest one of 2 methods.
The quickest would be to use a strimmer to scalp all the grass to the ground then lay down cardboard covered by well-rotted garden compost or cheap compost (terreau) when they start with spring offers and plant into that.
The second is to use clear plastic to cover the ground but you need hot sun which then burns or bakes the plants and seeds near the surface. That will take a bit longer and means you have to wait for hot sunshine. Then proceed as above with the cardboard and compost.