One cannot tell without a special stethoscope called a fetoscope (or at the very least applying one's ear directly on the mother's belly) if a fetus is "weak".
There is no way that Eli could determine by just palpating the abdomen of the deceased woman that the fetus is "weak": at this stage it is either moving (very improbable as it is not getting any oxygen) or not moving (probably dead).
A baby born by emergency Cesarean-section from a deceased mother cannot cry with strength a few seconds after being delivered. It would likely be blue, floppy and probably would not even be breathing by itself.
It is not possible for a fetus to survive but a few minutes after the pregnant mother's death as the oxygen-filled blood is pumped by her heart through the placenta.
The first use of the ghillie suit is reportedly during the Second Boer War by British scouts. This would be more than 35 years after the scene in The English.
The baby looks more like a 6 or 9 week-old than a new born.
The Merriam-Webster dictionary states wop's first known use was in the United States in 1908, while the show takes place in 1860.
Cornelia says "Noo" Orleans instead of the English pronunciation "Neeoo" Orleans.