It has been interesting seeing how list-members variously interpret idée
fixe.
Of course, the word is French, and has passed into probably every European
language with a slightly different nuance.
I can assure you all, however, that accusing someone of an idée fixe is used
to native English speakers to designate someone mentally deranged:
http://education.yahoo.com/reference/dictionary/entry/idee+fixe
It means not just a fixed idea but an idea held against evidence against it
or with complete lack of evidence.
Therefore, it is an aspersion against the person who holds it.
A strongly held idea is simply a conviction.
Patrick