Just to clarify, even though there are female/feminine translations of dog and cat, they are often not used anyways because their feminine forms have vulgar and obtrusive second meanings. Most native French will only use "chien" or "chat" in formal situations because of such.

araignée is a feminine noun, and there is not a different form of the word that is used when refering to a male araignée

There are also many other animals that are the same as this - that there is only a masculine or a feminine form.

There are not many of these in relation to animals, however there are a few.

i.e.
for dog: (male or female) chien (ne) m f
for cat: (male or female) chat (te) m f
for donkey: (male or female) âne (sse) m f
for duck: (m) canard ; (f) cane
for rabbit: (male or female) lapin (e) m f
for wolf: (m) loup ; (f) louve
for lion: (male or female) lion (ne) m f
for bear: (male or female) ours (e) m f

Also see: https://www.duolingo.com/comment/5871/Question-Difference-between-chat-and-chatte

This is similar to proffessions and nationalities for people.

Thank you for asking this question.
I will put it in my homework pile to write more about this. For it is a very interesting topic (for me).

It applies to a variety of different nouns, including often pet nouns.
Being that there is a feminine and masculine form.

I will be back shortly with more information.