In English, "They are expecting THE sixth child" would usually refer to a child other than one of their own. For example, they are having a birthday party for their little boy. They've invited six other kids. Although their son is getting really impatient, they don't want to start the fun yet because they are "expecting the sixth child" to arrive at any moment. "Expecting A sixth child" is accepted, since that is generally understood to mean "expecting their sixth child."
Common usage is "expecting," and using "expect" causes the sentence to sound incomplete.
"Expect" could be used, however, in a sentence that provides more information -- "They expect their sixth child in November." Even there, I suspect that "expecting" would likely be used more often, though "expect" works as well.