Se noyer dans un verre d'eau

Julie had one task for the office potluck: bring whipped cream.  But halfway to work, she realized she'd left it in the fridge at home.  What followed was... dramatic.  She spent the rest of the day spiraling in self-inflicted guilt, Googling “how to recover from social failure,” and seriously considered quitting her job.  Maybe even starting a new life in a whipped-cream-free monastery.  Meanwhile, her coworkers were happily eating pie with ice cream instead.  In short: Julie had  drowned in a glass of water - elle s'est noyée dans un verre d'eau.

It’s the French way of saying someone loses their mind over a tiny problem. Really tiny.  Similar to the English “Don’t make a mountain out of a molehill.”
In this expression, the verb se noyer is conjugated normally - that is, according to the subject and the tense required by the context.  The expression is not inherently rude or offensive, but it’s mildly teasing. It implies someone is being overly dramatic or incapable of handling a simple situation, so tone and context matter;  funny and harmless in the right setting, but not ideal when someone’s actually having a rough time.

Origin

The expression has been used in French since at least the 19th century to criticize people who lack perspective or resilience when facing minor difficulties.  The image comes from the absurdity of someone drowning in something so small and harmless as a glass of water.   

Why a glass of water?  Because it’s ridiculously small.  If you manage to drown in a glass of water, either you’re a microbe, or you have an extreme talent for panic.
The image is meant to poke fun at people who turn a drop of drama into a flood of despair.

Examples

Camille a paniqué toute la matinée parce qu’elle avait perdu ses clés… qui étaient dans sa poche. Elle se noie vraiment dans un verre d’eau!
Camille panicked all morning because she thought she lost her keys… which were in her pocket. She really falls apart over nothing!

Thomas a eu un exercice de maths un peu difficile et a fondu en larmes. Il se noie dans un verre d’eau !
Thomas got a slightly tricky math problem and burst into tears. He panicks over so little!