FlyerTalk Evangelist and Ambassador: The British Airways Club
Join Date: Jun 2008
Location: Somewhere between 0 and 13,000 metres high
Programs: AF/KL Life Plat, BA GGL+GfL, ALL Diam, Hilton Diam, Marriott Gold, blablablah, etc
Posts: 33,241
The only way you can easily find out is by calling whichever seller you bought the ticket from (AF if you bought direct, or the TA or OTA you used otherwise). As Goldorak says, there is no "general" answer to your question, not even knowing the booking bucket.
In other words, the literal answer to your question is no, nobody can tell you if upgrading is possible and/or how much it would cost except people who have access both to your reservation and to GDS with the full list of fares and availability on your flight.