I was watching a movie in my french class about the 1914 Christmas ceasefire and in the movie, the opposing armies were close enough to hear each other sing, play the bagpipes, etc. and the trenches appeared to be just a few meters in between. Is this accurate and if not, how far away would they have been.
It would depend; it's impossible to determine 'average distance' when we're talking about a front nearly 500 miles long and going through numerous different terrains and regions of importance. On that note there wasn't some kind of standardized distance to keep from the enemy and they were not about getting precise measurements between the two trenches.
We have primary source material showing that if we're talking about a very hot area frontline trenches could be within 20 yards of each other. In 'quieter' areas, especially in the Southern region of France and less important British sectors, the distances could be 500-700 yards apart completely reasonably. There were times when the French and Germans alike could just send horse carriages and even trucks into no mans land to gather dead, lay barbed wire, etc. because there was literally zero risk of enemy snipers. We have an equal amount of primary source material showing that it wasn't artillery that killed you but the fact that enemy machine gun fire an sniper fire was constantly being laid down and a man couldn't poke his head above the trench without being hit.
It's, unfortunately, a question of "it depends" -- you would have to be more specific than that. 100-200 yards would be a good 'ballpark' estimate if I was pressed though.
"Life and Death in the Trenches of the First World War", Andy Simpson
"Tommy: The British Soldier on the Western Front", Richard Holmes
It would depend on the lay of the land. The minimum practicable distance was about 15-30 metres, or the distance a 'bomb' (grenade) could be thrown. Trenches could be this close but would be thinnly manned, or just patrolled. Much over about 500-700 metres and it was scarcely necessary to establish a trench, as this was about the limit of accurate rifle fire for most troops. Of course, trenches could be re-occupied and new ones nearby rebuilt: at Poizieres during the Battle of the Somme, for instance, an existing German trench system was partially occupied and men fought one another over an extended period within what was the same trench. Barricades within the trench called 'stops' were built and defended in such cases, while heavy artillery fire turned the trench system into a chaos of holes.
Saps and approach trenches would be dug out into No Man's Land before offensives to provide a 'jumping off point', and such positions could also support forward outposts.
In short, there were many things that affected trench positioning, but given a situation where two sides are fairly free to dig in parallel to one another, they would get as close as possible, without being so close that the trench itself was highly dangerous or so close it could be easily 'rushed'.
Sources: The Great War, Les Carlyon, Death's Men, Derek Winter, Eye-Deep In Hell, John Ellis