« Il y a l’alarme-incendie qui s’est déclenchée ce matin, on a failli faire une crise cardiaque tellement on a eu peur ! »

If you want a slang, banlieues speech register version :

Ce matin, l’alarme incendie, elle nous a fait flipper notre race !

Beware that the register of flipper sa race is probably quite the opposite of the English expression “scare the bejesus of someone”…

A still colloquial but less distinctive alternative can be:

Elle nous a fait flipper grave !

Quebec slang with (mild) expletive “crisse” French would be:

L’alarme d’incendie ce matin nous a fait peur en crisse!

In addition to other answers:

“L’alarme incendie nous a fait la peur de notre vie!”

You can also use “foutre la trouille”, which usually conveys a notion of suddenty:

L’alarme incendie nous a foutu la trouille [de notre vie] !

Although “foutre” is quite informal here, it would not be considered as vulgar/slang in this context, unlike in “va te faire foutre !” (“fuck off!”).

Adding “de notre vie” (“of our life”) enforces the feeling of severity, although it is usually not used in the litteral sense.