This is definitely something I've experienced before on my own Vel Satis :-)
For 18 months after I bought it, the driver's door on mine also clicked. The door didn't seem to get any worse, but it was annoying and a bit embarrassing when neighbours were around. So I asked my local Renault dealer about it when I took the car for its last MoT, and they fixed it for me, by fitting a new check strap – as you suspected. It wasn't cheap at about £80 from what I can remember, so you may want to shop around or look on eBay, or at breakers yards, like you said.
So if it's any consolation, it should be a problem you can live with for ages, but if you feel it getting worse of want it fixed, yes, you need a new check strap.
If you like, I can look at the paperwork to see what the part number was, and try to find somewhere they can supply one for you?
I always like to approach Renauly Parts Warehouse as Michael there is so friendly and helpful – http://www.renaultpartswarehouse.co.uk