Hi miket
Yes, you should be able to remortgage for €100k to invest in shares or a property fund. You should use the opportunity to shop around for the cheapest mortgage and not necessarily just stick with your current provider.
You should go for interest only, if it is backed by readily realisable investments. You are borrowing at 3% to invest in a product with an uncertain, but expected postive return. If the security of your salary allows you to take this risk, go for it.
Unfortunately, you will not be able to set the interest costs against the income or capital gains from any shares or unit funds. That is one of the advantages of investing in property, you can set the interest paid against the interest received.
There are some geared funds. They buy property within the fund and borrow within the fund. So the fund gets tax relief on the interest paid. I don't think that the higher interest charges and high annual management charges, and initial charges justify this.
In general if you have cash lying around, you should pay off your mortgage. But if you just about to invest, I would not bother.
Brendan