Just to add that I agree you are best off buying a proper perfume bottle and atomiser than a household one.
With most commercial perfumes a crimp spray attachment will have been used - these are a pain to remove - it can be done with the aid of a pair of pliers but don't attempt it until you have your replacement bottle on hand as you won't be able to replace it once it's off. For the same reason make sure you've got a bottle (or bottles) big enough to hold all the remaining juice in your faulty bottle.
I prefer screw-on atomisers, so that's what I use for my own offerings: it gives the customer maximum choice when it comes to decanting and re-filling.
A final thought - if it was one of my perfumes that had a dodgy sprayer I'd send a replacement sprayer to the customer without hesitation. You might try contacting Givenchy (assuming it isn't dodgy because you broke it obviously) - they won't be able to send a replacement sprayer if it's a crimp-fitting, but they might just send a new bottle . . . worth an email I'd have thought.