I want to buy a few booster pack from a local shop that only gets them in French. Is it generally acceptable to show up to a tournament with cards in different languages?
Under official Magic, they're all the same card regardless of the printed language. From the comprehensive rules:
201.2. A card’s name is always considered to be the English version of its name, regardless of printed language.
From the tournament rules:
It is not required that players play with cards that are printed in the native language of the area in which the tournament is being run. If a player needs to know what a card does, either because it is in a language they cannot read, or it is a textless printing, they may call for a judge and ask for the Oracle text.
As per Sarnthere's answer it is legal to use non-English language cards in official tournaments. However though legal, some people find the use of non-English cards in predominately English speaking areas a bit unsporting. It is not an uncommon strategy for some people to use non-English cards to obfuscate their board state.
For example: In a tournament game a friend of mine won because he had a German Dragonlord Kolaghan and his opponent forgot about its second ability:
Whenever an opponent casts a creature or planeswalker spell with the same name as a card in his or her graveyard, that player loses 10 life.
Even though his opponent had asked for clarification from a judge on what the Dragonlord did earlier in the match, he had forgotten the ability in the heat of the moment. This lead to him playing a creature that was also in his graveyard. My friend let the creature resolve after which he stated the ability triggered, the opponent took 10 damage and the following turn my friend won the game.