There isn't a simple functional causal relationship between interest rates, inflation and currency rates.

And in fact, I think you have it exactly backwards in this case.

Many countries have dollarized their economies - replacing a local currency supported by high interest rates with the US dollar which has even lower interest rate than EUR - as a tool to tame inflation or kill hyper-inflation. Other - small non-EU countries have adopted the Euro for the same reason.

And with the same result - a massive fall in inflation.

This isn't just theory, this has been observed to work over and over again.