I'm posting a second link for you which is a forum you can join, and where you can have your button i.d.'d by french collectors. It has a way to translate and it is free. It seems there was a huge variety of French Marine buttons from the early (1803-12 and earlier) period, an they existed in every imaginable style within a very brief and often overlapping period. I doubt very much that your university professor could have immediately known what your's was, considering some of these are still a mystery in France. It also seems from the following scans that even the University people mentioned in my above post may have misidentified a button they found at an early 1800's site. At any rate I've posted several scans for you which show clearly a style similar to your's with many variations. The style rope border is the problem so far. ..............Oh No!

I have just discovered that the scans do not appear!!!! You must get them for yourself! Here is how:......
1) Go to the first page (translated) 2) Press the research tab. 3) enter in the first box marine 4) examine each link individually and look at the similarity and huge number of different styles in a single few years (and this is a tiny sample!)
Hopefully one of the savvy members of this forum will know how to post the actual photos?
priodhttp://translate.google.com/translate?hl=en&sl=fr&u=http://labanquedesboutons.forumactif.com/venez-vous-prsentez-afin-que-l-on-puisse-vous-souhaiter-la-bienvenue-f1/bonjour-tous-les-amoureux-des-boutons-militaires-francais-t17.htm&ei=ZrueSorfO9PflAeC94GtDQ&sa=X&oi=translate&resnum=10&ct=result&prev=/search%3Fq%3Dbouton%2Bmilitaire%2Bfrancaise%26hl%3Den
http://translate.google.com/transla...ev=/search?q=bouton+militaire+francaise&hl=en
http://translate.google.com/transla...ev=/search?q=bouton+militaire+francaise&hl=en
http://translate.google.com/transla...ev=/search?q=bouton+militaire+francaise&hl=en
http://translate.google.com/transla...ev=/search?q=bouton+militaire+francaise&hl=en
http://translate.google.com/transla...ev=/search?q=bouton+militaire+francaise&hl=en
http://translate.google.com/transla...ev=/search?q=bouton+militaire+francaise&hl=en