Translation:After two weeks, a puppy opens its eyes.
In French, it will always be "les yeux" when referring to body parts, and in referring to "a puppy", you may confidently use "its eyes".
Even people must use “ouvre les yeux”, the expression in French always uses the definite article with body parts instead of possessives.
In English, if the gender of the puppy is known, “his” or “her” can be used and “their” is certainly not wrong for the plural.
“les” does not translate to “her”. The expression “After two weeks, a puppy opens its eyes” translates to the French version in which all body parts use the definite articles, so « Après deux semaines, un chiot ouvre les yeux. » You cannot use « ses yeux » there.
In French the assumption is that the body parts always refer to the person or animal previously mentioned. In English, we cannot say “
We open the eyes.” It just sounds weird to us, but in French it would sound weird to say « Nous ouvrons nos yeux. »