Question: Were both King Baggot and Jean-Pierre Melville French filmmakers?

Context articles: Two Men in Manhattan
Le Silence de la mer (1949 film)
King Baggot
Les Enfants Terribles (film)
Jean-Pierre Melville
Code Name Melville
Jean-Patrick Manchette
Army of Shadows
Le Samouraï
King Baggot (cinematographer)

Two Men in Manhattan (French: Deux hommes dans Manhattan ) is a 1959 French film-noir directed by Jean-Pierre Melville.
 The film stars Melville (who also wrote the screenplay) and Pierre Grasset as two French journalists in New York City searching for a missing United Nations diplomat.
Le Silence de la mer (English: "The Silence of the Sea" ) is a 1949 film by Jean-Pierre Melville.
 It was Melville's first feature film, and was based on the 1942 book of the same name by Jean Bruller (published clandestinely under the pen name "Vercors").
 The story, which takes place in 1941, concerns the relationship of a Frenchman (Jean-Marie Robain) and his niece (Nicole Stéphane) with a German lieutenant, Werner von Ebrennac (Howard Vernon), who occupies their house during the German occupation of France.
 The film was actually shot inside Bruller's own home outside of Paris.
William King Baggot (November 7, 1879 – July 11, 1948) was an American actor, film director and screenwriter.
 He was an internationally famous movie star of the silent film era.
 The first individually publicized leading man in America, Baggot was referred to as "King of the Movies," "The Most Photographed Man in the World" and "The Man Whose Face Is As Familiar As The Man In The Moon."
Les Enfants Terribles ("The terrible children") is a 1950 French film directed by Jean-Pierre Melville and based on Jean Cocteau's novel of the same name.
 The first feature film of Melville, "Le Silence de la Mer" (1949), attracted the attention of Jean Cocteau, who commissioned him to direct the film version of "Les Enfants Terribles".
Jean-Pierre Melville (] ; born Jean-Pierre Grumbach; 20 October 1917 – 2 August 1973) was a French filmmaker.
Code Name Melville (original French title: Sous le nom de Melville) is a feature length documentary about Jean-Pierre Melville, directed by Olivier Bohler and produced by Raphaël Millet for Nocturnes Productions in 2008.
 Its world premiere took place in November 2008 at the Golden Horse Film Festival in Taipei (Taiwan).
 It has been shown on French channel CinéCinéma Classic in March–April 2010, and on Belgian channel La Deux (RTBF) in May 2010.
 It is the first feature documentary about Jean-Pierre Melville since he died in 1973.
Jean-Patrick Manchette (19 December 1942, Marseille – 3 June 1995, Paris) was a French crime novelist credited with reinventing and reinvigorating the genre.
 He wrote ten short novels in the seventies and early eighties, and is widely recognized as the foremost French crime fiction author of the 1970s - 1980s.
 His stories are violent, existentialist explorations of the human condition and French society.
 Manchette was politically to the left and his writing reflects this through his analysis of social positions and culture.
 His books are reminiscent of the "nouvelle vague" crime films of Jean-Pierre Melville, employing a similarly cool, existential style on a typically American genre (film noir for Melville and pulp novels for Manchette).
Army of Shadows (French: L'armée des ombres ) is a 1969 French film directed by Jean-Pierre Melville.
 It is a film adaptation of Joseph Kessel's 1943 book of the same name, which blends Kessel's own experiences as a member of the French Resistance with fictionalized versions of other Resistance members.
 "Army of Shadows" follows a small group of Resistance fighters as they move between safe houses, work with the Allied militaries, kill informers, and attempt to evade the capture and execution that they know is their most likely fate.
 While portraying its characters as heroic, the film presents a bleak, unromantic view of the Resistance.
Le Samouraï (] ; "The Samurai"), also known as The Godson, is a 1967 French-Italian crime film co-written and directed by French filmmaker Jean-Pierre Melville, starring Alain Delon, Nathalie Delon, and François Périer.
 It was Melville's first film in color.
Stephen King Baggot, A.S.C. (born August 15, 1943) is an American cinematographer.
 Baggot is a member of the American Society of Cinematographers.
 He is the grandson of actor/director of the early 20th century, King Baggot.