was watching, was keeping an eye on
Tu la surveillais comme un faucon.
You were watching her like a hawk.
— Assurance sur la mort (1944)
Puis je le suivais à l'épicerie et je le surveillais.
Then I followed him to the grocery store and kept an eye on him.
— Un Soleil (2019)
Je les surveillais.
I was watching them.
— Harry Potter et l'Ordre du Phénix (2007)
Je surveillais sa valise.
I was watching his suitcase.