Formal:
* Continuons. (Most literal translation)
* Poursuivons. (More formal and means "let's pursue")
Informal:
* On continue. (Most common and informal)
* Continuons comme ça. (Means "let's continue like this")
* Allez, on continue ! (More enthusiastic and means "Come on, let's continue!")
Specific contexts:
* Continuons notre discussion. (Let's continue our discussion)
* Continuons à travailler. (Let's continue working)
* Continuons ce que nous avons commencé. (Let's continue what we started)
The best choice will depend on the specific situation and your relationship with the person you're talking to.