RR
EU has no right to search any countries ships going to Syria unless they in EU territorial waters. The definition of EU territorial waters of course would mean that member states cede their territorial rights to the EU to do as they wish, something unlikely to happen.
Any attempt to do so has no legal basis and no different to an act of piracy on deciding to search ships in International waters with no legal basis in International law.
Course precedence would allow other countries right to do so as well be it military or civilian craft.