Hi Cymru...
In answer to your question, the simple answer is YES!
New unopened fragrance normally lasts at least a year or more if kept properly, but opened perfume will eventually go off as it is based on a volatile liquid that will evaporate.
The smell will definitely be a give away (but as you say, it could just be an unpleasant scent) but also check the colour to see if it has darkened significantly or thickened.
The usual advice to prevent this happening is to ensure your perfume lid is secured tightly and not placed in direct sunlight or near a heat source.
Unfortunately there is little you can do with it once it has gone off - if I were you, I'd play safe and throw it away!
Sorry I can't be more positive. Fi