As I was googling French Songs I found The book of French songs, by John Oxenford and Louisa Stuart Costello, published in London in 1877.
The book has been digitized by Google and it's 'Translator's preface' is so appropriate and eloquent, here is part of it:
Where there is so abundant a song literature as that of France, a small volume like this cannot be free from sins of omission. Perhaps every reader may have in his mind some song that he will think ought to have had a place here, and that he will be surprised to find has been passed over. To all objections on the score of omission I can only answer by remarking, that where from a huge mass a very limited quantity is to be extracted, the work of selection must always bear an arbitrary appearance. However, I believe I am not going too far when I say that, in spite of the narrow compass of the collection, no class or style of song (fit for the general reader) has been left unrepresented...'
The last sentence does not apply to My little book of French songs as I am certain many styles of songs and many authors and performers that the reader tremendously enjoys or feels should be included have been left out of my personal, subjective and arbitrary selection.
That's why there are many pages that were left blank within this book, so that you can complete it with your very own choices.
The book does not contain the lyrics nor the music but they can be found easily on line.
My very limited but I think strategic objective is to offer a selection of songs and performers that you can use to start your own collection.