General translation:
* L'esprit de la vie (literally "the spirit of life")
More specific translations:
* Le souffle de la vie (literally "the breath of life")
* L'élan vital (literally "the vital impulse")
* La force vitale (literally "the vital force")
The best translation will depend on the specific context of your use.
For example, if you are talking about the spiritual aspect of life, "l'esprit de la vie" would be a suitable choice. If you are discussing the physical essence of life, "le souffle de la vie" or "l'élan vital" might be more appropriate.