The UK people would say - Yes your warranty is valid in all European countries (just to get the sale). The Beko people in France (if there are any) will say No, your warranty is worthless here.
Warranty and the responsibility for it rests with the vendor - a shop chain may have a contract for repairs with a national company - their engineers however will not be expected to go abroad to service machines.
I used to work for an international IT comapny. People would buy equipment in whichever European country was offering the best deal and then ship it to where it was required. Warranty was owned by the sales manager of the selling country. The sales managers of the destination country would laugh at any warranty claim and refuse it outright because they got no recognition (profit or comission) for it.
I don't think the UK Sale of Goods Act is recognised in France.
Peccavi, May 2009