From my more distant (US) perspective, the classism in France is different. It's based on what university you went to, not who your ancestors were.

It's based on social codes more than anything, similar to other countries. There are preferred vectors of transmission for such codes. In France some schools my play a part but I don't believe it's so segregated. The role of grandes écoles is overblown and they're not nearly as influential as Ivy League schools and Oxbridge are in the US and UK. I'd say the high school you went to is probably a more important factor, as are the extra-curricular activities you were doing growing up, in deciding which class you fit in.

Could you expand in this? Do you mean material way of life or how people treat each other socially.

For me it's a combination of how people talk about others 'below' their class, and how much social mixing between the classes there is - but I realise that this is very hard to measure. Just my 2c having lived in UK, Europe, and US.

The French literally executed away their class system.

Of course they didn't, unless you are using some extremely narrow and historical definition of "class". France still have significant wealth inequality and rent-seeking, so by most modern definitions of "class" they certainly have a class system.

The UK has a formal class system that's actually encoded in law (peerages, knights, royal family, etc.) France got rid of all that.