Why were French maids apparently so common outside France?

This was common, but only in Anglo-Saxon families, especially British ones, and only rich ones (of course). The reason they were French are what follows:

• First, maids could not have been non-Europeans for obvious reasons (idea of a superior civilization): rich families of that period would search for people of similar ethnicity and religion to take care of their children
• French was an important language during that period: many rich Englishmen spoke French, travelled to France and Swiss
• Other candidates were Scandinavian or German, but France provided more because it was a very rural society, were it was usual for girls to go to service of others while male peasants stayed in the countryside. Contrary to an urban and/or industrial civilization where women found employment

I think a few good ideas were already given above, but here is what I can gether from my readings online:

Throughout Europe, working on service was a common thing but then, through time it became more and more of a feminine sector.

A lot of this is explained in this article about servants by Bridget Hill: "perhaps most notably in postrevolutionary France, there was a marked decline in the number of servants employed by the nobility and an increase in the number employed by the middle classes. Another change was the increasing mobility of servants. In response to the chance of a wider experience, better wages or conditions, or the hope of more sympathetic employers, domestic servants constantly changed places."

Besides that, it is important to note that France has historically been renowned for their extravagance and fashion, and so the higher classes of other countries would look at France for preferred traits rather than employ people of other backgrounds who would "devalue" the aesthetic of their own household.

An interesting read about that in on this Why are the French so Chic article.

I can only speak to Anglo-Saxon usage of french maids, but there are several reasons they were preferred, but before I got into these I would just like to say that the majority of french maids severing the gentry were not poor peasant girls, for the most part they were from the lower-middle or middle classes or sometimes the upper middle class (though those served mainly as governesses) and they were educated in schooling and manners, now of course cheaper maids from the lower classes were available, but they were mainly used by middle class English who were imitating what the upper classes were doing.

The first reason for their selection was their knowledge of proper french, in addition to the head ladies maid, they often helped as governesses (depending on their social station in France) or tutors to educate the younger Anglo-Saxon gentry. Secondly, they were thought to have a better idea of fashion, hair-styles, and general trends in france, which was very valuable to the lady of house, as most fashion was coming from France at that time. Finally, the French were seen as racially acceptable to the English, and though maids from India, China, etc, have been attested to, the vast majority of English housekeepers came from W. European countries, ie France, Belgium, Netherlands, etc... There were Irish housekeepers too, but they usually occupied to lowest tier of the staff.

To slightly expand on this, the servants of a household had a clear line of rank, the french maid, who primarily served the lady of the house, was in the upper ranks usually ranked about 3rd or 4th behind the butler, stable keeper/gardener and sometimes the cook. Her primary responsibilities were dressing/bathing/perfuming the lady of the house and accompanying here to various lady functions. The lady of the house, for the most part was able to choose the maid on her own, this bypassed the traditional hiring practice of having the butler handle that. So it seems a bit obvious if she got her pick, she would choose someone with her interests, fashion, hair styles, art, couture, continental manners, etc... which a french maid could provide.

Also at this time period there was much upheaval in France, leaving once upper-middle class families in destitute, for some taking a maid/governess job was a way to keep them out of poverty and to create connections with English society that could be useful.