French there is a process called liaison, where final consonants are omitted unless the next word starts with a vowel. Would it be accurate to say that the English indefinite article (a/an) is an example of this as well, or are these two separate words that mean the same thing?
They're both examples of a broader concept sometimes termed sandhi, basically meaning 'phonological processes occurring to glue words together'. Whether they're both examples of liaison depends on your point of view and on how you want to use that term.
If you use the term liaison very loosely to mean something informal like 'a consonant introduced between two words to join them together', then you could maybe class English a~an as an example of this. You might also class as liaison in English the 'r' sound you get between vowels in e.g. 'law-r-and order', 'Canada-r-in summer'.
But, from a more technical point of view, if you start to try and model the actual phonological processes that are happening in French liaison, the phenomenon has some fundamentally different characteristics in French compared to English. For example:
So, it depends on how specifically you want to compare 'like with like' when applying the term to both languages. For reasons such as those above, I personally would avoid doing so.
[*] Actually, there are speech errors when this occasionally isn't true.
A is a variant of an, which was itself a variant of one. An started to change into a from the 12th century onwards before a word that began with a consonant. In some dialects, it is still found even before words that begin with a vowel.
What this means is that an is not so much an instance of liaison as that a is an instance of elision, the process whereby sounds get left out. The /d/ sound in mashed potatoes, for example, gets lost in speech, although in that case the spelling is unchanged. Liaison, as Neil suggests, occurs in combinations such as ‘law and order’, where intrusive /r/ is sometimes heard before ‘and’.