There are simple ways to remove errors to get your protractor tests to start running against you vue backend however the big issue you will face is that the ephemeral IDs that each framework uses for the HTML they generate will be done differently , this will most likely cause selenium to fail to find specific page elements to test, this could be very time consuming for a large suite , possibly more than re-write.
Protractor was written for angular but not vue , whilst vue started out from the same place they have gone different ways , especially angular2.
The recommended test tool for vue is Jest , i would recommend taking a spike task to see how complex it is to migrate a set of reasonably complex tests to Jest , you might find it at lot easier. You could run subsets of both sets of tests if you find there isn't a clear winner.
The goal in test is always to demonstrate the functionality as simply and reliably as possible.