Beech can be kept narrow and slim and if you buy the copper variety you'll have added colour. If you prune it at the right time it doesn't drop its old leaves in autumn and they add extra privacy until the new buds burst in spring. However, if your ground is damp, you're better off with hornbeam.
Privet is fine. If you are in a mild area you could try escallonia or maybe a mix of different plants. Escallonia will provide pink or white flowers in summer and stays evergreen except in a harsh winter. Check this site to see if your conditions are suitable - https://www.rhs.org.uk/plants/popular/escallonia
As @Fairygirl says, autumn is the time for planting bare root hedging and there should be plenty of choice from local GCs or nurseries online. They will be small to start with but, as longa s you prepare the ground well, they get away very quickly and are much cheaper than potted plants. See here - https://www.rhs.org.uk/advice/profile?PID=377
Vendée - 20kms from Atlantic coast.
"The price good men (and women) pay for indifference to public affairs is to be ruled by evil men (and women)."
Smaller plants establish, and grow away, far more quickly than large ones, so it's never worthwhile buying bigger specimens. Around 3 feet [1 metre] is a good size
It's a place where beautiful isn't enough of a word....
I live in west central Scotland - not where that photo is...
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Privet is fine. If you are in a mild area you could try escallonia or maybe a mix of different plants. Escallonia will provide pink or white flowers in summer and stays evergreen except in a harsh winter. Check this site to see if your conditions are suitable - https://www.rhs.org.uk/plants/popular/escallonia
As @Fairygirl says, autumn is the time for planting bare root hedging and there should be plenty of choice from local GCs or nurseries online. They will be small to start with but, as longa s you prepare the ground well, they get away very quickly and are much cheaper than potted plants. See here - https://www.rhs.org.uk/advice/profile?PID=377
I live in west central Scotland - not where that photo is...