Translation of "Inquiring" in French

Upon inquiring, I learned that she was out.

En me renseignant, j'ai appris qu'elle était absente.

The police were inquiring into the suspect's past.

La police fouillait le passé des suspects.

I wrote to everybody inquiring after their health in the hot season.

J'écrivis à tous et m'enquis de leur santé lors de la saison chaude.