This research is concerned with studying and investigating the assignment of the contract, regulated by the new French law of the contract, issued according to the ordinance n° 2016-131 dated February 10, 2016, concerning reforms of the law of contract, general regime and proof of obligations. This assignment is as an agreement by which a party to a contract, the assignor, may assign his or her status, quality or contractual position as party to the contract to a third party of the original contract, the assignee, with the agreement of his own contractual partner, the debtor of the assignment (the assigned). And the study compared it with the assignment of the right, regulated by the Iraqi civil code No. (40) of 1951. The problematization of the research lies in the shortage and insufficiency of the Iraqi civil code, as a result of the lack of both the principle of the assigner's co-obligations or joint obligations with the assignee, as well as the principle of the legal assignment of the contract, authorized by the law in some particular cases. This study has adopted to the analytical comparative methodology of the legal research, and the main finding of this study is the importance of both of the above-mentioned principles in the Iraqi civil law. The researcher suggests some relevant recommendations to the Iraqi legislator, the most important of which is the advisable enactment of these two principles in the Iraqi law.