Jersey.
This used to be a major holiday resort for honeymooners after the second world war.
They use the pound so Euro is not a problem, and there is not VAT (or it is very low cant remember) so prices are cheaper.
Flights will be fairly cheap, and it is only a short flight, probably less than an hour.
The capital St Hellier is a fine compact city with loads of quality hotels and lots of places to eat.
It is a small island so very easy to get round by hire car, or the buses are excellent.
You could certainly have a budget honeymoon in Jersey.