Suzy, Kit, where we live in the Jura, "would you like a drink?" means "would you like a pastis?" so we have got very used to this and pastis is my aperitif of choice. There is much discussion as to which brand is best - and which strength, how much water to add and whether to add ice or not. To be honest, we buy Lidl's own label and it's good.
A Swiss friend once visited with a bottle of locally-produced absinthe, which he happened to find (it was illegal to buy or sell it) and this is the real thing which pastis replaced while absinthe was illegal in France. Now it's less poisonous, without the wormwood, it is easier to get, and when we entertain we observe the ritual of a water dispenser full of ice, dribbling through tiny taps on to a sugar cube supported on a silver spoon over a glass with a dose of absinthe in it. Great fun, and delicious. Known as the "green fairy" this caused all sorts of health problems to the impressionists, but now while it may taste the same (allegedly) it is harmless in moderation.
My test of "French" restaurants in London has always been to request a pastis. If they offer Pernod they are just playing at Frenchness, if they ask which brand I'd like then I'm at home. I've never asked for an absinthe, but perhaps I should!