Is a traveller's allowance to drive on their native driving license renewable between EU countries?

http://vosdroits.service-public.fr/particuliers/F1459.xhtml#N1008E

According to this official site, for visitors staying 90 days or less, there is no requirement for the licensing jurisdiction to be the place where the driver resides. That may be an oversight, but still, if there's no such rule, it should be fine.

You might want to double check with the issuing state, however, to make sure the license hasn't been invalidated by the driver's having moved out of state. Most states have restrictions on incoming residents, but it is conceivable that there might be rules governing outgoing residents as well.

All the rules regarding non-EU licences are still defined country-by-country. The main piece of EU legislation regarding driving licences is directive 2006/126/EC and it says absolutely nothing on equivalence or recognition of non-EU licences.

In the case of France, the relevant rules are defined in Arrêté du 12 janvier 2012 fixant les conditions de reconnaissance et d'échange des permis de conduire délivrés par les Etats n'appartenant ni à l'Union européenne, ni à l'Espace économique européen.

The one-year delay runs from the moment someone becomes a resident in France, not the EU:

Tout permis de conduire délivré régulièrement au nom d'un Etat n'appartenant ni à l'Union européenne, ni à l'Espace économique européen est reconnu sur le territoire français jusqu'à l'expiration d'un délai d'un an qui suit l'acquisition de la résidence normale en France.

Another important requirement is that the licence must have been issued by the country where the holder had his or her “habitual residence” at the time the licence was issued (the goal is to make sure French residents don't go abroad to get a licence to circumvent a driving ban or another requirement of French licences). In practice, if you are a citizen of the country that issued your licence, you don't have to prove this:

Apporter la preuve de sa résidence normale […] Les ressortissants étrangers qui possèdent uniquement la nationalité de l'Etat du permis détenu ne sont pas soumis à cette condition.

(The text reads “Foreign nationals who have only the citizenship of the state that issued the permit” but if your friend shows her US passport and the licence, I doubt she will be asked anything else.)

Note that the licence must in principle be in French or accompanied by a certified French translation.

I'm not convinced there is a general rule for this that could be applied across all EU members, as different member countries have different rules and exemptions. The EU is not a collection of states in the same way that the US is.

In your specific case I don't think she would be allowed to use her American license. From the French Licensing Guidelines if using a license issues outside of the European Economic Area (EEA) it can be used for up to 12 months and must meet the following requirements

It must be valid;
It must have been issued by the country in which you normally resided before moving to France;
It must be written in French or be accompanied by an official translation.

From your question I think point number 2 could not be meet.

Additionally point number 3 would be a problem unless you have an international driving permit http://www.aaa.com/vacation/idpf.html

Whilst I am aware the above web page refers to moving to France, I can't find any mention of other rules for visiting so I think they come under the same category as such a trip would by definition be under a year.