No, 1-12 are influenced by the old base 12 Germanic/Norse system, which is why -teen starts at thirteen, same as in German (11: elf, 12: zwölf, 13: dreizehn, 14: vierzehn & so on)... The -teen for 1x in english is also a carryover from this, being threeten, fourten, fiveten etc. with only numbers over 20 having their orders reversed - German has something similar with "und" only appearing in numbers over 20. English did historically too, eg. "four and twenty blackbirds".

Base 20 was historically used for large numbers though, eg "four score and seven years" by Abraham Lincoln, which was a poetic way of saying 87 inspired from Psalms 90:10, which says "The days of our years are threescore years and ten; and if by reason of strength they be fourscore years, yet is their strength labour and sorrow; for it is soon cut off, and we fly away." in the King James Version, which reflects that using base 20 for large numbers (and not just 80) was not uncommon in the 17th century.

Seems like they're not, although I get your thought process. If we take Old English (which was English before the Norman conquest) and modern Swedish (since Sweden was never conquered by anyone from France or the Romans) as comparisons, we have

Eleven: OE endleofan, Swedish elva Twelve: OE twelf, Swedish tolv Thirteen: OE threotiene, Swedish tretton Fourteen: OE feowertiene, Swedish fjortun

I think you can see the pattern. These actually all have similar common ancestors going into Proto-Germanic, so they're way older than the French influence on English.

Since other Indo-European languages like German and Russian do the same thing as English where the line between "one word numbers" and "two word numbers" is 20 to 21, I suspect that originates waaaaay back in the history of these languages