A 1 day overstay, especially if you can show that it was caused by circumstances outside of your control, is almost certainly not going to cause any issues - although I would make sure to have some form of proof of the change when exiting the country. However at the end of the day it is technically an overstay, and thus there may be negative consequences - even if they are unlikely.
Personally I would not be accepting the change to the following day, and I would suggest contacting the airport and seeing what other options are possible. Make it clear to them that the flight a day later will leave you in breech of your Visa, as this will basically force them to take action.
As this flight is from an EU location, Regulation (EC) No 261/2004 (commonly referred to as EU261) applies. This regulation specifies what the airline must do in the event of a cancellation like this, and what compensation is due. Depending on exactly when they notified you of the change (in particular, whether it was more or less than 14 days before departure) then it's possible that a non-trivial amount of compensation is due to you.
Google for "eu 261" will find you plenty of information regarding this regulations and specifically compensation in a format that might be easier to read than the actual regulation itself.