Here's what we know.
What is Levothyrox?
It's a drug that replaces a natural hormone called thyroxine. The thyroid gland is supposed to produce this hormone on its own, but fails to do so in sufferers of thyroid disorders.
The thyroid plays an important role in growth, as well as in a person's nervous system and metabolism.
As a result, Levothyrox is a vital drug for three million patients in France, according to France's ANSM agency, which oversees the safety of medicines and health products.
Sufferers of hypothyroidism - when the gland produces too little thyroxine - can use the treatment to slow down the effects of the disorder. These effects can include memory loss, slowing down of the heart, intense fatigue, drowsiness, depressive states and weight gain.
How was the formula changed?
In March 2017, the Merck laboratory removed lactose from the treatment and replaced it with citric acid and mannitol - a type of sugar alcohol.
The new formula was expected to be more stable and easier to tolerate than the existing drug.
The ANSM said "the new formula is biologically equivalent to its predecessor" meaning the new medicine is guaranteed to be as safe and effective as its previous incarnation.
What are the patients saying?
"We are facing a major crisis," Chantal L’Hoir, founder of the French thyroid disorder association told France Info.
"I had cramps in my thighs like I've never had before, to the point where I couldn't walk," she said. "I didn't dare to drive anymore because I was dizzy.
"I was more tired than I've ever been. Since stopping the treatment, I've had a new lease of life."
Others have complained of suicidal thoughts, memory loss, hair loss and palpitations, some of whom have been on the treatment for decades without complaint until the formula change, according to Ouest France.
"We're not scientists, but I find the lack of attention it's getting from the medical world deplorable," said L'Hoir.
A petition to stop the prescription of Levothyrox has received just over 97,000 signatures, as of Thursday morning.
Is everyone on Levothyrox affected?
No. The vast majority of people using the treatment are not presenting any side effects, Le Figaro reported.
It has been reported that some patients are even feeling better since the change in formula.
Why are the side effects happening?
According to doctors, it seems unlikely that there is an intolerance to the new ingredients in the drug, particularly when they are present in many medicines and even sweets, in the case of mannitol.
But it's possible that changing the formula has changed the way the body absorbs levothyroxine, the main ingredient in the treatment.
What are the medical authorities saying?
An emergency number was set up by the ANSM on Wednesday, in a bid to respond to concerns from people using the treatment.
If you're concerned, you can call 0800 97 16 53 from Monday to Friday 9am - 7pm.
Thyroid disorders leave people more sensitive to changes and exacerbate anxiety, professor Jean-Christophe Lifante, a thyroid specialist at Lyon-Sud hospital, told Le Parisien.
"It could be having effects on certain patients, but we need to calm the controversy because the majority of them are only temporary."
Meanwhile the ANSM is enquiring into the undesirable effects, however "the first results show that there is no difference in terms of safety between the previous version of the treatment and the one now being prescribed", it said.