If you can't call it aspirin just say acetylsalicylic acid instead.

Besides it's use as an analgesic, aspirin is used in small doses to thin the blood when there is a possibility of clots forming.

I have travelled to France many times (and even worked there for a while) and have never been asked by customs if I was carrying aspirin, paracetamol or any other medicinal drug. If medicines were banned for import for personal use, it would be very arkward for anyone who used regularly prescribed drugs for asthma, diabetes, heart conditions etc.