Hi, for what my opinion is worth, my choice of name would be:
Alice Elizabeth Frances
However, Eleanor or Cecile would be lovely as a first name. The former was one of our greatest Queen Consorts (Eleanor of Aquitaine), and it could always be the French version of the name, Alienor, which is what Eleanor would have been named at birth and while she was Queen Consort of France to Louis VII. With Cecile, this would be a poignant reminder for Prince Philip, who had an older sister, Princess Cecile (1911-1937), who was married to the last titular Grand Duke of Hesse & by Rhine. They had 3 children and the Princess was pregnant with her 4th child, when, on November 16 1937 she, her husband, her mother-in-law and her 2 sons (Alexander & Ludwig) were killed when the plane they were travelling in crashed into a factory chimney in thick fog over Steene, Belgium. Tragically their orphaned daughter, Johanna, who was left at home, died in 1939 from meningitis.