New find.

I've googled this as I thought it was a garlic variety because my mother-in-law has something blooming now thats very like it in bright yellow.
I think it's Tulbaghia Violacea

www.rhs.org.uk/plants/18484/tulbaghia-violacea/details

https://www.gransnet.com/uploads/talk/202406/medium-560800-1000020718.jpg https://www.gransnet.com/uploads/talk/202406/medium-96441-1000020717.jpg

Not good photos but really lovely in real life and much taller.
I just took these in a hurry to look up the flower.
I think it's Alium Moly

Thank you, that's helpful.
I'm not surprised I was drawn to the plant, because apparently it is sometimes known as pink agapanthus? My favourite flower is agapanthus.
It sounds like it likes full sun and sandy soil.
The plants here in France are certainly more advanced this year than in UK, even though they have also experienced copious amounts of rain. My lavender back home had no sign of colour a few weeks ago.
The yellow star version looks pretty in your photos too, NotSpaghetti.

It's actually about 35 or 40 cms tall.
Yes it's lovely.
I love agapanthus too.
I think your "walk" plant will grow here. It does look pretty.