You probably know the general way in which a(n) and the are used. You use the definite article the if what is mentioned has already been mentioned or is known to the reader/hearer. Otherwise you use an indefinite article. The area of the territory has not been mentioned before, so an is appropriate.
The portion ",an area with more than four times the size of France,"
is an "interruptor" inside the sentence
"The Louisiana territory was purchased from France in 1803".
Its function is to explain what the Louisiana territory is.
You would most probably have no difficulty in understanding why a non-definite article was used if you turned the whole sentence into a relative:
"The Lousiana territory, which is/was an area with more than four times the size of France, was purchased from France in 1803".
Similar cases: "The lion, a kind of huge cat, is ..."; My mother in law, an extraordinarily minute woman, is/was...
Hello rttw, there can also be another reason why 'the' doesn't work here (apart from 'first mention' explained by natkretep above). 'The' (definite article) appears to be defining Louisiana here. There is only one area more than four times the size of France, and it's Louisiana. This, of course, is not correct, as there are many areas or territories in the world which can be described as more than four times the size of France.
Paris, the capital of France .... There's only one capital of France, it's Paris.
Louisiana, the area more than four times ... There's only one area more than four times the size of France, it's Louisiana.