What you have heard is correct, although there is an on-going experiment into full legalisation of the practice known as remonter les files (riding between lanes of slow-moving traffic) in several departments. See the facing page about owning a scooter for more on this rule, which is limited to riding on roads with a central reservation and speed limit of 70kph or more.
Otherwise, it is not strictly legal and it is possible for an insurer not to pay out, according to sources including the French insurance brokers Euro-Assurance.
Insurance non-payment is not automatic and insurers consider the circumstances and your overall conduct and that of other road-users. However riding between lanes could lead to them concluding that you were fully (or partly) responsible for the accident.
Also while police usually tolerate the practice if carried out prudently, they occasionally fine a two-wheeler rider for it. The most common basis for this is ‘overtaking on the right’, which can be subject to a €135 fine (€90 if paid promptly) and the loss of three points. However the motorcyclists’ lobby group FFMC encourages people to contest such fines and says it can advise on this.
Despite this almost all two-wheel riders do it and FFMC argues that in a jam it is actually safer as if there is a pile-up then scooter and motorbike riders could otherwise end up “like the meat in a sandwich”.
The usual advice is to do it with care, at no more than 20-30kph faster than the traffic (50kph maximum), leaving around 10 metres between your two-wheeler and the next (you should never overtake another two-wheeler travelling between lanes).
Only go between lanes when all lanes on your side of the road are jammed and do it between lanes furthest to the left if there are more than two.
Of course, you should also respect the usual road rules such as the overall speed limit and not crossing a continuous white line.