Legal cohabitation

The simple answer is no. However it's potentially a lot more complicated than that depending on a variety of factors. Try the site www.notaire.be here:
http://www.notaire.be/se-marier-vivre-ensemble/la-cohabitation-legale/le...
Essentially each partner is the legal owner of their own finances and assets, but if you can't prove who own's what, then they are considered as jointly owned property.
If you buy something yourself, it belongs to you, if you buy it jointly, it belongs to each of you jointly, if you can't remember or prove who bought it, it is owned jointly.
Of course all this depends on whether you wrote and signed a convention de cohabitation that says otherwise.
If you're talking about small items, and not much money, then get over it and move on. If it's lots of money, or items that would be difficult or complicated to split (like a house or car) then you're only real choice is to negotiate, (or in the worst case, hire a lawyer, although you may be better seeing a notaire first.)

I wrote the first answer assuming that you may be in a legal cohabitation and breaking up. Of course, if you aren't, and are thinking about it, you should also be aware that legal cohabitation implies the same rights and obligations as marriage. Therefore, a lot more than just your current finances and assets should be considered. For example, you will be liable for each others debts, and you and your partner will be entitled to a part of each others inheritance should either of you die.
Get legal advice.