Registration of a fishing vessel under the Luxembourg flag is subject to more than 50% ownership by EU residents or EU-incorporated companies, and the captain of such ship must be a person whose nationality is that of one of the Member States of the European Union.
"Art. 4. Definitions [...]
Ship: for the purposes of the implementation of this Law, all ships with a tonnage of at least twenty-five tonnes which are used, or are intended to be regularly used, for the transport by sea of persons or things, or for fishing, towing or any other gainful seafaring activity, shall be considered to be ships. 
[...]
Art. 5. Field of application
Ships which are owned to the extent of more than 50% by residents of the European Union or by commercial companies which have their registered office in a Member State of the European Union, together with ships chartered on a bareboat basis and ships operated by such persons, shall be eligible for entry in the Luxembourg shipping register, provided that all or a significant part of the management of the ship is carried on in Luxembourg.
[...]
Section 2 - Provisions concerning ships[...]
Art. 20. Command of ships
The command of a ship flying the Luxembourg flag shall be entrusted to a person whose nationality is that of one of the Member States of the European Union and who is the holder of a diploma awarded by a school of navigation that is recognized in Luxembourg. Derogations from this nationality requirement may be granted by virtue of a specific authorization by the Minister in special cases, and in particular where the needs of commerce or of seafaring justify such a derogation, or else in the light of the origin of the ships which are applying for registration.[...]" (Act of 9 November 1990 to Establish a Luxembourg Maritime Register, Mém. A58 of 12/11/1990; as amended by the Act of 17th June 1994; Articles 4, 5 and 20 [unofficial translation])
Act of 9 November 1990 to Establish a Luxembourg Maritime Register, Mém. A58 of 12/11/1990; as amended by the Act of 17th June 1994; Articles 4, 5 and 20
[<a href="https://legilux.public.lu/eli/etat/leg/loi/1990/11/09/n1/jo">Act</a>],[<a href="http://www.maritime.lu/sites/maritime.lu/files/files/pdf/maritime-act-1990_en.pdf">Act_Eng</a>]