Hi,
French is my native language.
"I'm just taking a guess here, and I hope some native French can support this, but I think that you can basically look at the end of the word to check which particle is needed. However, I already noticed that there isn't really a rule for this."
There are no rules ... sometimes, I don't know myself if word is feminine or masculine. Because it can "sound like" feminine (It's case most of the time) but be masculine ...
The only solution is to train your "ear" (I know, it's not really nice :D)
<So that seems pretty random, but words with "-eau" for example seem to have "le" most of the time.>
That's correct ;) I'm thinging but I don't see word with "la" before a name with an end in "eau". :)
So, in conclusion :
La porte
Le tableau