Did you buy it mail order? If you did, the firm in France will not be able to claim VAT exemption for something sent to the UK. You won't have to pay VAT, they will. The "no VAT" was probably just a sales gimmick.
If you bought it while you were in France, they should have charged you VAT. If they put it through as an export sale, their tax man will catch up with them eventually, but you won't have to pay VAT on it.
Once we leave the EU, everything changes. If you buy mail order, you have to pay VAT and import duties and that's normally collected by the carrier (Royal Mail, DHL etc). If you buy in person and it doesn't come within the customs allowances, you need to go through the red channel when you return to the UK and they'll charge VAT and import duty (assuming they can be bothered).