This quotation derives from Gaspard Gourguard, a French soldier who spent much time with Napoleon during his exile on St Helena. In 1899, more than 40 years after Gourgaud's death, his private journal was published (in French). In his entry for the 9th of January 1817, Gourgaud transcribed Napoleon as saying:

J'ai fait ce que j'ai pu pour améliorer le sort des bâtards, des malheureux bien innocents et qui sont pourtant déshonorés, mais on ne saurait pas beaucoup tenter pour eux sans porter atteinte à l'institution du mariage. Peu de gens, alors, se marieraient. Autrefois, en même temps que sa femme, on avait des concubines et les bâtards n'étaient pas méprisés comme ils le s[o]nt de nos jours. Je trouve ridicule qu'un homme ne puisse avoir légitimement qu'une seule femme. Quand elle est grosse, c'est comme s'il n'en avait plus. On n'a plus de concubines, c'est vrai, mais on a des maîtresses, ce qui dérange bien plus les fortunes. Je parle pour les gens aisés, car les pauvres n'en pourraient nourrir plus d'une. En France, les femmes sont trop considérées, elles ne doivent pas être regardées comme les égales des hommes, et ne sont, en réalité, que des machines à faire des enfants. Pendant la Révolution, elles s'insurgeaint, s'érigeaient en assemblées, voulaient même se former en bataillons: on fut obligé de réprimer cela. Le désordre se fût entièrement mis dans la société si les femmes étaient sorties de l'état de dépendance où elles doivent rester. C'eût été des luttes, des combats continuels. Un sexe doit être soumis à l'autre ...

My translation (apologies for any inaccuracies):

I did what I could to improve the lot of the illegitimate children, the unfortunate innocents who are nevertheless dishonored, but it wasn't possible to risk much for them without killing the institution of marriage. Few people, then, would get married. In the good old days, men had concubines and a wife at the same time, and illegitimate children were not held in so much contempt as they are these days. I find it ridiculous that a man should not be able to have more than one legal wife. When she's fat, it's as if he doesn't have a wife any more. True, we don't have concubines any more, but we do have mistresses, who mess up [men's] fortunes even more. I'm speaking of the well-to-do, since the poor can't feed more than one [wife]. In France, women are considered too [much], they shouldn't be seen as the equals of men, and, in reality, are nothing more than machines for making children. During the Revolution, they rose up, set themselves up in assemblies, even wanted to form battalions: we had to put a stop to that. If women had left the state of dependence where they should remain, disorder would have taken over society. There would have been continuous fighting. One sex must submit to the other ...