I've found a family in Chambers Co Al in 1850 that may or may not be who you are looking for.

pages 335b &336a
Alexander S Foster 38 SC
Elizabeth A 25 (illegible)
William W 7 Al
Mary A 5 "
Hannah 3 "
Francis A 1 month "

Although Elizabeth A's place of birth can't be positively read, it is different from her husband's and son William W's. The enumerator consistently used ditto marks for the same place of birth. What I can see for Elizabeth's place of birth could read Lousiana.

If I have found the correct families in 1880 Choctaw Co Al...
In 1880 Francis shows his father born in SC and mother in La. Same for sister Mary after she marries James E Turbeville. Mother Elizabeth shows La in 1880 in the Turbeville household.

Hope this helps. I tried rootsweb and LDS for Alexander and nothing came up. No relation, just had a little time.