Can a professor take a full-time 12 months industry job (get fully paid) while on one-year sabbatical?
The only legal rules that are likely to apply here are the contractual rules for the terms of the professor's employment with the university, combined with the university's policy/contract relating to sabbaticals.  Whether or not this is allowed would depend on the terms of the sabbatical, as set out in the appropriate university policies and employment contract.