Thank you xiphophilos. I realised after I posted that I should have checked the matrix numbers. The matrix number on the DG is the same as the HMV, and the other number etched into the run out area is 48816 which matches the Victor matrix shown in DAHR.
I will add the record as you suggest, and thanks for pointing me towards the DAHR which I haven't come across before.
If you compare other "Disque Gramophone" records (listed under "Gramophone" here) with British HMV releases, you'll probably find other re-couplings too. Originally, "My Mother's Eyes" by Waring's Pennsylvanians was released on Victor 21857 in April 1929 whereas Johnny Hamp's Kentucky Serenaders released "Where is the Song of Songs for Me?" on Victor 21838 in March 1929 (info from DAHR1 and DAHR2). DAHR does not contain a version of "My Mother's Eyes" by the Kentucky Serenaders, so this could simply be a printer's error on the French label.
The only way to know for sure if the versions of "My Mother's Eyes" on both records are the same is to compare the matrix numbers. And of course it would be great if you could enter your record into the database, preferably even with images. Then we could all see what you are talking about.
I have a "Disque Gramophone" version of this record - made in France but with the Nipper trademark and the same catalogue number (B prefix, not the usual K prefix for France). My Mother's Eyes is shown on the label as by Johnny Hamp's Kentucky Serenaders, and does not sound like Waring's Pennsylvanians. Just a different version for France?