I think the female assasin wanted some action at the creek.

It seemed to me that she was interested. She was definitely being flirtatious, though whether with intent to merely probe his reactions and character or to actually have a quick run, I am not sure. I suspect, though, that there was not much more intent than a one time or occasional thing as opposed to their becoming a Mr. & Mrs. Smith.

watching it again (Netflix Instant!) i think there's something else going on. I think she's (1) checking to see if others in town know he frequents this place, and (2) she's trying to get his guard down so she can kill him. But he's all business, spilling the wine, etc.

Think about it: she commissioned the gun, possibly for this job, maybe for a future job. Pavel calls her and tells her "Listen Carefully" AFTER Clooney calls up and quits the game. THAT is when Pavel decides to kill him, i think - though he may have told Mathilde to kill him when she has a chance.

But think about the picnic - she has the gun, and some rounds, in her possession. She's earned his trust (somewhat) by not shooting him as he walked away to do the auditory test (and by letting him shoot at her, she shows that she trusts him). It's all a con! She's lulling him into a sense of security, and, if he's willing to strip down and do the horizontal mambo, she can take a quiet moment to put a pill in his ear. The additional tasks she gives him - the case, make more rounds, modify the suppressor, etc - she could easily do elsewhere (either herself, or thru another source).

She knows she's gotta kill him at some point, i think. It's possible Pavel tells her to kill him from the jump, or after the phone call. But the scene can definitely be read both ways: either she's super-impressed with him, and wants some action, or she's lulling him into a sense of security, for a hit (then or later).