"I know them."
Translation:Je les sais.
leur is an indirect object pronoun...it means TO them. Used...je leur ai dit - I told them / I said to them OR je ll leur donne - I'm giving it to them. LES is the direct object pronoun and only means him or it. So je la regarde - I'm looking at it. Je les mange. - I'm eating them. So LEUR could not work here because connaitre would take the direct object pronoun...les since the les / they are getting the action and it is not happening to them.
Well, asemaika's answer is kind of simplified. To expand on it, connaître and savoir both mean "to know," but they have different flavors in their meanings (if that makes sense).
Connaître is used when you know people, or are familiar with something. Savoir is the general "to know" verb. It is also the only one that can be used with verbs. Ex: I know how to speak French / je sais parler français.
This may help more: http://french.about.com/od/grammar/a/savoirconnaitre.htm
EUX = is a generalized "them" -- what flowers do you want?? --- EUX (them).
Your answer may probly sound like:
"I (may/kinda/sorta) know (some very vague) them"
----> "who are we talking about?" would be the next natural question (from confusion).
TO QUOTE: Dannilo3 (above) Connaître is used when you know people, or are familiar WITH something. Savoir is the general "to know" verb. It is also the only one that can be used with verbs. Ex: I know how to speak French / je sais parler français.
Technically that would be correct if the 'them' in the sentence referred to objects rather than people. The context of the sentence isn't too clear, but nevertheless know that connaître is used to say that you know someone or are familiar with something, whereas savoir is used to say that you know how to do something or know something as by memory.
I'm not sure whether a moderator will fix this sentence to allow both, or make the context clearer. :/
Btw @asemaika gives a good answer above, too. A question similar to yours was asked.