http://www.geopatronyme.com/ shows only one Middleditch born in France between 1891 and 1990. This person was born somewhere between 1916 and 1940 in Maroeuil, Pas de Calais, France. (very close to Arras). This could be a child of Charles Gage Middleditch?
Charles and brother Harry James's WWI attestation papers are at:
http://www.collectionscanada.gc.ca/databases/cef/001042-100.01-e.phpwww.ellisisland.com shows a couple of hits for Charles (G) Middleditch, resident of Maroeuil. In 1919 he appears to be entering NY with his wife, Cecile Alex. Middleditch. He returns in 1922 - gives his father in law as Mr A. Percheval, at Marocuil (sic), P.d.C., France.
In the 1919 the Ellis Island link to the manifest is broken; you can find the original manifest at
www.stevemorse.org. They are at Series T715, Roll 2675, Frame 645.
Charles G. Middleditch, 27, marine rock driller, Canadian/French, last residence Maroeuil
wife Cecilie Alex. Middleditch, 22, housewife, last residence ditto.
Relative Alfred Percival, Maroeuil.
They were headed to Amherstburg. Charles, at least, had previously been in the US, in Detroit in 1912. He is listed as b. Ridgetown and she was b. Maroeuil.
Interestingly if you go to
http://www.geopatronyme.com/ and put in Percheval you do find one hit in Maroeuil between 1891-1915.
http://www.planete-genealogie.fr/berrannice/veninpagnier/fiche/individu/?IndiID=123 - this is also very interesting. This would seem likely to be your Cecile's family but they list her with a different husband. They don't say when the marriage took place and one child is given a DOB of 1927 - so might she have remarried? Does this ring any bells?
Charles Gage Middleditch's full army records (available from Canadian Archives once you've found his attestation papers online) might give some interesting information.