If the flights were booked as 9W flights, then there should have been no issue.
If, however, they were booked as codeshares - even EY, for example - then there may be some other issue at play.
"Etihad Air Partners" is not a full alliance in the same sense that Star Alliance, etc, are, and lounge access may be more of an issue unless you are travelling on the "right" flightcodes.
Access to Etihad lounges can be problematic at the best of times. You may not be aware of this, but in Abu Dhabi, Etihad's status passengers that happen to be travelling in economy
do not have access to the Etihad lounges (there is a third party lounge provided, but it's not of the same standard).
It's also been reported here that the Etihad lounge in Sydney no longer accepts status customers travelling in Economy:
http://www.flyertalk.com/forum/etiha...ge-access.html
http://www.flyertalk.com/forum/etiha...ccess-syd.html
It could perhaps be that the Etihad lounge in Paris also now refuses customers that are not travelling in First or Business. I don't know for certain.
But it's probably more that the Alitalia Gold card will only get you into the Etihad lounges only when travelling on EY- or AZ-coded flights. (Remember - Etihad Air Partners is not a full alliance). When travelling on 9W- flights, it would get you into the Jet Airways lounges (where they are operated - the Jet Airways page on the Alitalia website lists them). That 9W uses the EY lounge in CDG means that 9W business pax, and 9W/EY status pax are covered - but not AZ (or JU/AB etc) status pax.
As for inputting the Frequent Flyer number, this seems to be more of an issue with Alitalia than with most other airlines (I've had trouble adding it to Air France/KLM bookings, too). May I ask - why did you/your wife not add the number yourself at the time of booking, or subsequently? Did you try, but were you also unable to do so?
In general, you should pad the number with leading zeroes until the system accepts it. In my experiences with Air France/KLM, this has sometimes involved making an 8-digit number (starting with a single 0) or a 10-digit number (starting with 000).