As a French learner, you have no doubt begun to see (if not been outright taught) that words that begin with vowels are treated differently than words that begin with consonants. Perhaps most obvious to the casual observer is the process known as elision, which is the contraction formed by many common words, such as je, le, la, que, ce, and de (to name only a few) when they come before words that begin with a vowel. Elision is the reason why, for example, even the biggest francophobe can be heard confidently uttering c’est la vie (that’s life!) and not ce est la vie.
Another thing that you probably know by now is that the French h is always silent. However, since French words that start with h are almost always followed by a vowel (heure, histoire, honneur, etc.), an obvious question to ask is: do we treat words that begin with h as we do words that begin with a vowel (since a vowel is the first sound that we actually hear)?
The answer is: sometimes we do and sometimes we don’t! The vast majority of French words that start with h are treated as if they start with a vowel (even though, technically, the French consider h a consonant). The French call the h at the beginning of these words an h muet (mute h). However, there is a relatively small group of "h words" that are treated as if they begin with a consonant (which they do!). The French call the h at the beginning of these words an h aspiré (aspirated h).
Ils ont été écrits comme ça, je pense, en un quart d'heure...
They were written like that, I think, in a quarter of an hour...
Caption 5, Bertand Pierre: Victor Hugo
In the caption above, we see that singer Bertrand Pierre says en un quart d’heure, forming an elision between de and heure to create d’heure. This is because heure, like most French words that start with h, begins with an h muet; it forms elision just as words that start with a vowel do.
Maladie qui ne l’empêche nullement d’être un sportif de haut niveau
An illness which in no way keeps him from being an elite athlete
Caption 4, Le Journal: Un sportif handicapé
On the other hand, the h in the word haut is aspiré; it is treated the same as other words that begin with a consonant. This is why we hear no elision between de and haut in the caption above. We hear three distinct words: de haut niveau, NOT d’haut niveau. (Put another way, h aspiré “prevents” the elision.)
How do we know whether an h at the beginning of a word is an h muet or an h aspiré? Unfortunately, there is no way of knowing just by looking at it! H aspiré words will usually have an asterisk or an apostrophe before them in French dictionaries. Also, lists of h aspiré words have been published that can be used for reference or (gasp!) memorization.
Other than that, exposure to fluent French speakers will hopefully help you build a “native-like” feel for which words are h aspiré and which are h muet. H aspiré words tend to be of “foreign” origin (“borrowed” from another language, e.g. le hockey), but this is not always the case, and even when it is, it is not always obvious.
Another common phenomenon associated with words that begin with a vowel is known as liaison, which has to do with pronunciation changes caused by certain types of words (contingent upon the letter they end with) when they precede a word that starts with a vowel. As you might have guessed, we also hear liaison occurring with h muet words and not with h aspiré words.
Passez par chez nous, restaurant “Les Héritiers”, n'oubliez pas c'est un “apporter son vin"...
Stop by our place, “Les Héritiers” [The Heirs] restaurant, don't forget it's a “bring your own wine”...
Caption 28, Les Héritiers: Les bonnes recettes - Part 1
Do you notice that when the chef says the name of his restaurant we hear something like "les-Zhéritiers"? That “z” sound is an example of liaison. We hear something similar in les heures (the hours), les histoires (the stories), and any number of h muet words.
In contrast, have a listen to the lovely lady from Le Mans we met one day in Manhattan’s Central Park, extolling the virtues of the fair city of New York:
Et les hamburgers sont meilleurs ici...
And the hamburgers are better here...
You will notice that we do not hear any “z” sound between les and hamburgers. This is because hamburger begins with an h aspiré—there is no liaison between the les and an h aspiré word, just as there is no liaison between the les and a word that begins with a consonant
The thing about most “rules” is that you know they will be broken! It is not terribly uncommon to hear native French speakers forming elisions and liaisons with some words that the dictionary tells us are h aspiré. For example, even though the venerable Larousse dictionary insists that hamburger is h aspiré, it is entirely possible to encounter French natives forming the elision l’hamburger, or saying perhaps un hamburger with a liaison, such that we hear it pronounced as “un-Nhamburger.”
Side note: We use the word “contraction” when describing “elisions” because our English readers are familiar with contractions such as “didn’t,” “don’t” and “wouldn’t,” and the similarities are obvious. Technically speaking, to a linguist or the like, a contraction and an elision are not exactly the same thing.