The English here has to be: It isn't the animals that get into the airplane but the people. We just can't say "Not the animals..."

"Not the animals get into the plane, but the people."

No, no, no.

The "not" should not be at the start of the sentence but with the verb. Are you talking about specific or general animals, people and planes?

"The animals do not get into the plane, but the people do." - if you are talking about a specific set of animals, people and a specific plane.

"Animals do not board planes, but people do" I think is what is trying to be expressed here.