As you're only starting out in life, you might be better putting the €2,000 spare each month into more liquid investments than paying off your mortgage - if you pay off the full €2,000 per month extra, chances are you'll never be able to get that money back again.
If you put the money into some kind of stock market fund e.g. Quinn funds etc, you'd be able to cash the money in if needed in the future when you start a family - after all, your mortgage repayments are quite small compared to your monthly take-home, so I doubt you desperately need to reduce the mortgage.
Don't forget also, you're unlikely to stay in (what I assume is) your first house for more than five years, so you'll need a hefty deposit when trading up - again this would point to keeping your spare cash in relatively liquid vehicles like the stock market.
However, first priority is to build up an emergency fund - given that you're both in the private sector, I'd go for up to 6 months' of living expenses e.g. mortgage, food, transport etc.
I note you're paying 12.5% into your pension - at your age, you can get tax relief on contributions up to 20% of your gross salary - you might look at upping your contributions to take maximum advantage of the tax relief available.