"Bitch" is a perfectly legitimate translation for chienne. It means female dog. It was a word long before it was a swear word. In fact, as a swear word it means someone who resembles or acts like a female dog.
It is still used by scientists, breeders, and veterinarians. It means female dog.
I don't think they should use "chienne" or "chatte" in the sentences at all, because they mean pretty much the same thing in French as their literal translations in English-- "bitch" and "❤❤❤❤❤" respectively. They're insults in French just as in English, and from what I've heard it's much more common to just use the masculine versions, even when talking about female dogs and cats...
It may be a cultural difference (British, over 60) but I don't find "bitch" in the context of dogs the slightest bit offensive. If there is no reason to specify the sex of the animal I agree that "dog" and "chien" are fine, but I could say "I looked after her dogs, both bitches..." without thinking I could offend anyone. Would people really find this deeply shocking? If they did, I would be careful in using it.
You can see adverts in supermarkets or on the web which say « donne chienne ». We need to know the sex of an animal in this context, so I would use “bitch” in English.
We use plenty of animal names, some sex-specific, as insults in English: ass, mule, bitch, dog, wolf, goat, cow, pig, rat, mouse, snake... I don't see what is so different about “bitch”.
Apart from the use of « chatte » in jokes, where the misunderstanding is the whole point of the joke, I don't see how anyone could confuse the two meanings. « Donne chatte » just means a female cat needs a home.
No, of course they're not offensive in those contexts, just like they aren't in English. But the point is that "chat" and "chien" are both perfectly acceptable words for female dogs and cats, and teaching those words FIRST prevents any misunderstandings or miscommunications for beginners.
For example, I would not teach specific animal terms to a beginning English learner at all, much less words like "bitch" and "❤❤❤❤❤" which are used vulgarly much more often than they are technically. Even when they are understood by their technical meanings in context, most native English speakers would first think of the vulgar meaning.
I believe you cannot avoid teaching/learning basic words for the mere reason they may have another slang connotation. On the contrary, I should say, because every single time one of these words appear here, there are learners to tell you it is also a dirty word. So, one shot, two birds. In addition, the French language being bi-gender in general, it is usual and perfectly natural that female dogs' owners refer to their animal as "ma chienne".
I don't think that more specific terms for animals, like "sow" or "mare" or "bitch" can be considered basic words.
And while French has genders, they don't necessarily have to match the subject's physical gender. Many occupations only have a masculine form, and females use that. Similarly, many animals don't have equivalent masculine and feminine forms, so you just add "mâle" and "femelle" to them (e.g. une souris mâle, un éléphant femelle.) I've heard people use "chat" to describe female cats way more than I've heard them called "chattes".