Biarritz is ,from my few visits there, no dearer than any other popular French resort -which ,if you are careful, is still cheaper than staying in Ireland. By "careful" I mean, for example, choosing plat de jour menus. You can eat a decent two course lunch for under a tenner and if you avoid the obviously deluxe restaurants you can have a fine dinner for well under twenty. (and there's always Macdonalds!)
Unfortunately, and this has always surprised me, when drinking wine in French restaurants you may pay nearly as much as in an irish restaurants even if you're surroudned by vine yards.
Local transport is good and cheap - neighbouring Bayonne 20 mins away -worth a days visit - is slightly cheaper to eat/stay. St jean de Luz 30 mins south on teh copast is to some people the nicest town on that coast. Again, eating on sea promenade restuarants is always dearer -but, i repeat, cheaper than here.
In 45 mins you're in Spain - San sebastian . Slightly cheaper than france.
Anyway september is a good time to avoid crowds and high hotel prices.
Slight chance of rain,though