Sauron has many spies
Sauron does not know the Fellowship’s path, but he is not without resources. His spies are everywhere, and the Fellowship can never be sure they are not being watched.
As Gandalf says earlier, many animals are spies of Sauron:
GANDALF: Be careful, both of you. The Enemy has
many spies in his service, many ways of
Further, Aragorn suggests that there are orcs in the area, many of whom serve Sauron:
ARAGORN: By nightfall these hills will be swarming with Orcs! We must
reach the Woods of Lothlórien. Come Boromir. Legolas. Gimli, get them
Lórien is the home of two elves of great power, Galadriel and Celeborn. In the film universe, Galadriel helped drive Sauron, in his guise as the Necromancer, out of Mirkwood. She was thus one of his greatest enemies. If the hills around Lórien were swarming with orcs, and Sauron had many animal spies, it would only make sense for them to watch the comings and goings.
Galadriel and Celeborn have their own means of perception
CELEBORN: The Enemy knows you have entered here. What hope you had in
secrecy is now gone. Eight that are here yet nine there were set out
from Rivendell. Tell me where is Gandalf? For I much desire to speak
with him. I can no longer see him from afar.
From this we can conclude that Celeborn had some way of perceiving things at a distance. It is thus possible that he noticed the movements of Sauron’s spies following the Fellowship.
We also know that Galadriel possesses her Mirror, which can show faraway events:
‘Many things I can command the Mirror to reveal,’ she answered, ‘and
to some I can show what they desire to see. But the Mirror will also
show things unbidden, and those are often stranger and more profitable
than things which we wish to behold. What you will see, if you leave
the Mirror free to work, I cannot tell. For it
shows things that were, and things that are, and things that yet may
be. But which it is that he sees, even the wisest cannot always tell.
Do you wish to look?’
The Lord of the Rings: The Fellowship of the Ring
As such, it is very plausible that (a) Sauron’s spies noticed the Fellowship enter Lórien, and (b) that Celeborn and Galadriel in turn noticed the spies.