Agreed. There should be a stick-shaker or similar to let pilots know the other control is being used. Maybe not the existing stick-shaker, since that's usually for stalls, but something similar.

I have no idea why the pilot-monitoring would have taken his controls. Or why the pilot-flying wouldn't have called him out for it. Possibly a seniority issue - we've seen similar issues before. Hopefully the french aviation authorities can determine the root cause.