Usually, people who endeavour to learn a language do so in the hope of being well-understood by its native speakers.
Where French is concerned, that hope borders on need – the French revel in the exquisiteness of their language; they do not take kindly to it being mangled.
That is no doubt a part of what drives your desire to speak French like a native.
As in the UK, it’s more common in France to run across regional dialects; when you come right down to it, there is no such thing as a French accent – much like there’s no true British accent.
Because France is a country of dialects, the French body governing linguistic matters has wrangled the elements of the language into Standard French, which is spoken with a region-neutral inflexion.
How can you master that unique French sound?
Mind your vowel groups: ‘ai’, ‘au’, ‘eu’, ‘oi’, ‘ou’.
The ‘ai’ combination sounds a bit like the English ‘eh’ sound and ‘au’ (also ‘eau’) sounds like ‘oh’. You try it: ‘mais’, ‘frais’, ‘marais’ (the ‘S’ is silent); ‘aube’, ‘Claude’, ‘jaune’. The frequently-used ‘eu’ sounds like the ‘e’ at the end of ‘the’. Your turn: ‘Europe’, ‘heure’, ‘peur’, ‘heureux’. The French ‘oi’ is more like ‘wah’: ‘oiseau’, ‘voire’, and ‘toi et moi’. The French ‘ou’ is different from the one at the end of ‘you’; it sounds more like the ‘oo’ in ‘boot’. Some words to practise with: ‘fou’, ‘jouer’, ‘doux’, ‘chou’.
Just as the English language has the ‘th’ sound to bedevil non-native speakers, French has it’s impossible letters to torture English speakers: R and U.
The R is guttural; to say it properly, you should sound like you are going to spit from the back of your throat. Beware, though, not every R is pronounced, especially not the ones at the ends of words.
To make the ‘U’ sound properly, pucker your lips as though you would whistle a tune and push the tip of your tongue to your bottom teeth.
Moving your mouth properly is critical to mastering French pronunciation.
Unlike English, French words do not require exaggerated mouth movements. Speaking French demands more precise manoeuvering of your tongue.
What about pronouncing diacritical marks?
They are indeed important, especially as they can change a word’s meaning: compare ‘la’ (definite article) to ‘là’ (‘there’). The mark doesn’t change how the word sounds.
Likewise ‘ou’ (‘or’) versus où (‘where’) – again, no pronunciation change, just in meaning.
The most critical mark, from a pronunciation perspective, is the accent tréma, used to show that two vowels next to each other should be pronounced individually.
Such cases exist in English, especially with words borrowed from French: naïve, coïncidence, and Noël. We don’t write the tréma but we still pronounce those words like the French do.
Improving your French-speaking skills will take time and practice; the best way to master French pronunciation is to work steadily and to get as much exposure to the language as you can.