The French verb "tenir" can indeed mean several different things. In the sense of "keep", here are some examples:
- tenir sa chambre propre = to keep one's room tidy
- tenir les aliments au frais = to keep food in a cool place
- tenir la porte fermée = to keep the door closed
- tenir sa droite/sa gauche = to keep to the right/to the left
Context has a significant influence in which verb you use. You would use "garder" in the sense of "to look after" (a person, a child, an animal). Examining "tenir" in context does not show it being used in the sense of "keeping" an animal. The Oxford French Dictionary actually suggests "avoir" in that sense. When "keep" is used, it is generally in the sense of "keep in check", "hold onto" (Il tient son chien en laisse = He keeps his dog on a leash), or sometimes "maintain" (Son appartement est très bien tenu = His flat is very well maintained) -WordReference. So look to context to help you decide whether you are "in charge of" the cat, or you are "holding" the cat.
"Garder" is used when you want to say "to look after" (someone or something). http://www.larousse.fr/dictionnaires/francais-anglais/garder/36086
I don't know if your comment is related to mine, but it's a good information anyway.
Likewise, I say that "Ella tiene un gato" is accepted in the French course in Spanish, though many disagree...
Tenir => Sostener, mantener( agarrado/asido), sujetar, agarrar, tener(?) => To hold, keep, maintain, sustain, grip/grasp, have(?).
By the way, wordreference↑ didn't include "to have" as a translation (neither main nor additional).
Please help. In English, "She keeps a cat." usually means she owns a cat, (usually expressed "She has a cat.") But "She holds a cat." is totally different. It means she has a cat in her hands -- any old cat. I'm not clear which of those two meanings "Elle tient un chat" expresses in French.
Basically, it means she is holding the cat. The French "tenir" has a wide range of applications and can include "avoir". The sense of "keep" for "tenir" is varied: tenir quelqu'un occupé = to keep somebody busy, tenir sa chambre propre = to keep one's room tidy, tenir les aliments au frais = to keep food in a cool place, tenir un accord secret = to keep an agreement secret, tenir la porte fermée = to keep the door closed, tenir une note = to hold a note (music), tenir une promesse = to keep a promise. Source: Oxford French Dictionary.
Sorry my attempt at humor fell flat. "Hold up" is not one of the uses of "tenir" unless you're talking about holding up your hands, your pants, your socks, or in a phrasal sense (to be plausible), e.g., cette explication ne tient pas = that explanation doesn't hold up. http://www.wordreference.com/fren/tenir
Hold on! You don't get to make an assertion like that and just walk away. State your case and provide your reasoning and resources. The FR "tenir" may be used in a variety of ways, including "to hold", "to keep" (an animal), and many, many other uses. http://www.larousse.fr/dictionnaires/francais-anglais/tenir/76386