A dime a dozen
The English word "dozen" means "about twelve" and comes from the French word douzaine, which means the same thing. (If you're talking about things that come in sets of exactly twelve (i.e., eggs) then it's probably fair to say that "dozen" means "exactly twelve." Otherwise, I'd say the meaning is more fluid.)
English doesn't have many "about X number" words. Another one is "a couple," which means "about two." (I don't think the meaning extends so far as "one" or "three," but I think it could easily mean anywhere between 1.5 and 2.5, if referring to a mass noun.) However, we still make the most of these two expressions, by employing variants such as "a half dozen" ("about six") and "a couple dozen" ("about twenty-four").
Back to French. The word douzaine comes from the word douze (twelve) plus the suffix -aine. The cool thing about -ained, though, is that it can be added to a lot of different numbers. So you can also say huitaine for "about eight" and dixaine for "about ten" and vingtaine for "about twenty."
You can't add -aine to any old number, though. It seems to be most common with numbers that are multiples of ten, but even then, there are some exceptions. In order to get a better grasp on the distribution, I did a Google search to see which forms are the most common. I ignored numbers which returned under 1,000 hits, graphed the rest of them logarthmically, and added notes for the ones with skewed results:
X = 1,000-1,300 hits on Google with the domain limited to sites ending in ".fr"
XX = 1,301-9,999
XXX = 10,000-13,000
XXXX = 13,001-99,999
XXXXX = 100,000-130,000
XXXXXX = 130,001-999,999
XXXXXXX = 1,000,000-1,300,000
XXXXXXXX = 1,301,000-9,999,999
XXXX - quatraine - from quatre (4) *
XXXX - septaine - from sept (7)†
XXXXX - huitaine - huit (8)‡
XXXX - neuvaine - neuf (9)§
XXXX - dixaine - dix (10)
XXXXXXXX - douzaine - douze (12)
XX - quatorzaine - quatorze (14)
XXXXXXXX - quinzaine - quinze (15)
XXXXXXXX - vingtaine - vingt (20)
XXXXXXX - trentaine - trente (30)
XXXXXXX - quarantaine - quarante (40)
XXXXXXX - cinquantaine - cinquante (50)
XXXXXX - soixantaine - soixante (60)
XXXXXXXX - centaine - cent (100)
*Also the name of a type of poetic stanza (i.e., quatrain)
†Also part of a town name (Savigny-en-Septaine)
‡Can also mean "about a week"
§Also the name of a type of prayer recitation (i.e., novena)
Of the fourteen words with more than 1,000 hits, half are based on multiples of ten. Of the seven numbers that aren't multiples of ten, there are none higher than 15. No compound numbers can take the suffix. (The three missing multiples of ten are all compound numbers in standard French. 70 is "soixante-dix" (lit. "sixty-ten"), 80 is "quatre-vingt" ("four-twenty"), and 90 is "quatre-vingt-dix" ("four-twenty-ten"). There are alternate versions of these numbers in the regional dialects of Switzerland and Belgium which aren't compound nouns: "septante," "huitante" and "nonante." I found around 500 hits for "septantaine" and around 100 each for "huitantaine" and "nonantaine," but it's hard to say how significant the results are, since "septante," etc., are, themselves, less common regional variants.)
I'm not sure what conclusion to draw, except that simple numbers take the -aine suffix better than complex numbers, and 100 ("cent"), seems to be the highest number that can do so. ("Mille" — 1,000 — is also a simple number, but I didn't find many hits for "millaine.")
Speaking of "a hundred" and "a thousand" (and back to English), I think that "a hundred" is also more vague than saying "one hundred" (likewise for "a thousand" and "one thousand). For example, if you say you've done something "a hundred times," it has a different feel than if you say you've done it "one hundred times."
I've been working on this post, off and on, for over a dozen days, so I think I'm ready to call it done.