Actually, eleven and twelve also seem to be derived from 10+1 and 10+2. Let me quote from the classic book Number: The Language of Science by Tobias Dantzig (1930, republished with nice foreword by Barry Mazur):
Indeed, there is no mistaking the influence of our ten fingers on the “selection” of the base of our number system. In all Indo-European languages, as well as Semitic, Mongolian, and most primitive languages, the base of numeration is ten, i.e., there are independent number words up to ten, beyond which some compounding principle is used until 100 is reached. All these languages have independent words for 100 and 1000, and some languages for even higher decimal units. There are apparent exceptions, such as the English eleven and twelve, or the German elf and zwölf, but these have been traced to ein-lif and zwo-lif; lif being old German for ten.
And presumably this was inherited in other Germanic languages. (English, German and Norwegian all belong to the Germanic subfamily of Indo-European; French belongs to Italic.) Note that we can still discern a trace of "two" in "twelve".
That answers your question, but note that there are traces of other bases in our number words:
It is true that in addition to the decimal system, two other bases are reasonably widespread, but their character confirms to a remarkable degree the anthropomorphic nature of our counting scheme. These two other systems are the quinary, base 5, and the vigesimal, base 20. […]
Many languages still bear the traces of a quinary system, and it is reasonable to believe that some decimal systems passed through the quinary stage. Some philologists claim that even the Indo-European number languages are of a quinary origin. They point to the Greek word pempazein, to count by fives, and also to the unquestionably quinary character of the Roman numerals. However, there is no other evidence of this sort, and it is much more probable that our group of languages passed through a preliminary vigesimal stage. […]
While pure vigesimal systems are rare, there are numerous languages where the decimal and the vigesimal systems have merged. We have the English score, two-score, and three-score; the French vingt (20) and quatre-vingt (4 × 20). The old French used this form still more frequently; a hospital in Paris originally built for 300 blind veterans bears the quaint name of Quinze-Vingt (Fifteen-score); the name Onze-Vingt (Eleven-score) was given to a corps of police-sergeants comprising 220 men.
Also, we do have words like "dozen" (12) and "gross" (144) (any others?) for a few numbers not divisible by 5 (because highly divisible numbers are useful), but these words are sporadic and do not form the basis for any number-naming system in English as far as I know.
Edit: On further research, even though it's undisputed that eleven and twelve come from 1+10 and 2+10, the actual meaning of the lif part seems uncertain. The Online Etymology Dictionary confidently says:
c.1200, elleovene, from O.E. endleofan, lit. "one left" (over ten), from P.Gmc. *ainlif- (cf. O.S. elleban, O.Fris. andlova, Du. elf, O.H.G. einlif, Ger. elf, O.N. ellifu, Goth. ainlif), a compound of *ain "one" (see one) + PIE *leikw- "leave, remain" (cf. Gk. leipein "to leave behind;" see relinquish). Viking survivors who escaped an Anglo-Saxon victory were daroþa laf "the leavings of spears," while hamora laf "the leavings of hammers" was an O.E. kenning for "swords" (both from "The Battle of Brunanburgh"). Twelve reflects the same formation; outside Germanic the only instance of this formation is in Lithuanian, which uses it all the way to 19 (vienio-lika "eleven," dvy-lika "twelve," try-lika "thirteen," keturio-lika "fourteen," etc.)
But the OED says that "left" is just one theory:
Etymology: Common Teutonic: Old English ęndleofon corresponds to Old Frisian andlova, elleva, Old Saxon elleban (Middle Dutch elleven, Dutch elf), Old High German einlif (Middle High German eilf, German elf), Old Norse ellifu (Swedish ellifva, elfva, Danish elleve), Gothic ainlif < Old Germanic *ainlif- < *ain- (shortened < *aino-) [one] + -lif- of uncertain origin. Outside Teutonic the only analogous form is the Lithuanian vënó-lika, where -lika (answering in function to English -teen) is the terminal element of all the numerals from 11 to 19.
The Old English, Old Frisian, Old Saxon, and Old Norse forms represent a type *ainlifun, apparently assimilated to *tehun [ten]. The theory that the ending is a variant of Old Germanic *tehun, Aryan *dekm [ten], is now abandoned; some would derive it from the Aryan root *leiq or < *leip (both meaning to leave, to remain) so that eleven would mean ‘one left’ (after counting ten.)