Several methods have been developed and tested worldwide. You will find plenty of scientific literature available on the various Posidonia transplantation methodologies and success rates in coastal environments.
As you are in AIx-Marseille you should look for contact with the GIS Posidonie and the Professeur Boudouresque in Luminy. As well you should try M. Alexandre Meinesz in NIce and also "les jardiniers de la mer" http://www.lesjardiniersdelamer.org/. You will find lots of informations.
You may transplant some shoots but it is not feasible to transplant a large surface of Posidonia meadows. Effectiveness of reimplantation is usually very low. See the attached paper for more information