Question: In French, some nouns are considered male and some female (le/la). Is there a way which can help me understand which grammatical gender to use with which noun?

Answer: 
You can't, really
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As I was learning French (English is my first language) the idea of gender of objects can be difficult to grasp. Genders are pretty much arbitrary and is something you just have to remember with each word (this means remembering it as *"une fenêtre"* rather than *"fenêtre"*).

You can also always listen for a [*liaison*](https://en.wikipedia.org/wiki/Liaison_(French)). But usually when speaking with a fluent speaker this can be quite subtle, and difficult to listen to.

General Rules
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That said, they are *some general* patterns which can be used to distinguish the gender of a noun but these **are not rules**, and are only generally followed:

* Things originating in France *tend* to be feminine. e.g. `une crêpe`, or `une pizza`
* Things originating in America *tend* to be masculine e.g. `Un burger`

**BIG DISCLAIMER:** These **are not rules at all**, these are just observations I have made.

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### Spelling

Nouns ending in the following tend to be masculine:

* `ge`
* `le` (that aren't `-lle`, `-ole`, `-ale`, or `-ule`)
* `me`
* `re` (that isn't `-ure`)
* `phe`
* `age` source: @bleh

Nouns ending in the following tend to be feminine:

* `on`
* `é`
* `eur`

[[source]](http://www.languageguide.org/french/grammar/gender/rule.html)

Feminine nouns tend to have `e` at the end too but *many* masculine nouns also have `e` at the end

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While some genders *tend* to have certain endings, there isn't any definite cut and dry to determine the gender of a word without memorizing it. You *can* memorize some common endings though to make better guesses. [This question on French.SE](https://french.stackexchange.com/q/2616/7385) might provide more information on this.
On a more practical note, [here](https://drive.google.com/file/d/0B5iHCwiV-v7RLVRLVVZxX0xQQnM/view?pref=2&pli=1) is a cheat sheet for french gender, and [the accompanying article](http://www.languagecrawler.com/2015/06/cheat-sheet-for-learning-gender-of.html) suggests that *"glancing at this seven-page chart every once in a while helped solidify things"*.