It has been proposed that:
L'Enfant's "design of radiating avenues and monuments was significantly influenced by his time growing up at Versailles, France, where his father had been employed as a sculptor". (From http://www.geocities.com/CapitolHill/2233/upcoming.htm.)
"The plan of the city is based on principles employed by Andre Le Notre in the palace and garden of Versailles, where L'Enfant's father had worked as a court painter, and on Domenico Fontana's scheme (1585) for the replanning of Rome under Pope Sixtus V." (From http://sc94.ameslab.gov/TOUR/lenfant.html.)
L'Enfant designed a city similar in layout to the then French capitol city of Versailles. The Capitol in Washington sits in a position similar to that of the palace in Versailles, the White House (originally called the President's House) in the position of Grand Trianon, and the Mall is like the Parc. (From http://home.earthlink.net/~docktor/wmslogo.htm.)
Here is a 1789 map of Versailles, aligned with the North at the top. While it is true that it is similar to the DC map, there are many more differences than similarities.
First we see that "La Croix" is about 19 degrees off of a north-south alignment, while the DC grid is aligned to due north (astronomically and not by compass; by Ellicott).
Next we see that the avenue from the Trianon does not run to the Palace, while Pennsylvannia Avenue connects the White House and the Capitol Buildings in the DC map.
There are no avenues radiating to the west that would correlate to the so-called "compass" in the DC map. The avenues radiate to the east at Versailles.
The major difference, it would seem, is the fact that the L'Enfant map features an "L" shape and not a cross. Although other features have been added in the 20th Century that lend themselves to the cross shape, these features were not present in the planning map; and although filling in wetlands was definitely in the plan from the beginning, there was nothing in the early maps to indicate the possible direction of future growth of the city.
I have seen nothing to indicate that the Planners laid out a map saying that, it looks like this now, but we envision it looking like this in the future.
What does look like the Versailles map is the drawing of the 1901 McMillan Plan for the "renovation" of the Mall area.
The idea was that "the original plans of Pierre L'Enfant had been largely unrealized in the growth of the city" (from The 1901 Plan for Washington D.C.), what ever that might mean; so "the commissioners sought obtain a sense of cultural parity with Europe" and "to revitalize the capital city through the monumental forms of the Beaux-Arts style".
Note this patently insane statement, considering that the McMillan plan was seen as a continuation of the L'Enfant Plan:
"The McMillan Plan of 1901-02, named for Senator James McMillan, the commission's liaison and principal backer in Congress, was the United States' first attempt at city planning."
"The means to these ends was the 1901 plan. The group began their research for the comprehensive city plan by visiting the "great cities" of Europe. Vienna, Paris, and the town planning of Germany were their destinations in an attempt to recover the spirit of L'Enfant. The commissioners were particularly impressed with Paris. The broad Parisian avenues and gardens of Versailles were a great influence on the men, and with their predilection for the Beaux-Arts style, an understandable influence on the final plan."
So we see that rather than it being L'Enfant who was influenced by Versailles, it was those who sought to "save" his plan who were impressed by it, and sought to emulate it.