Switch off power when 0v is sensed / Short to ground
An output that shorts to ground when active is commonly called an NPN output (like the transistor).

It will be easiest to configure this so that the relay is energized when when the output is active. Simple connect the other side of the relay to 12v. That's the opposite of what you're asking for, but if you rewire the relay so that it's normally closed you will get a similar effect.

If you don't want to do that, because of power draw, or some failsafe issue, you will need another component or 2. Configure a mosfet with a pullup so that it is energizing the relay by default, then use the pull down to turn the mosfet off when the smoke detector output goes low.

Whatever you do, it's a good idea to add a flyback diode across the relay.