Ok, if you are a UK resident you can file a Small Claims Court case. You can do this electronically for a minimal cost. ~Air France must respond to this or they will get a default judgement. At that point, you will have the right to seize their property to have the judgement enforced. Of course, they will settle before then, but just image the pleasure of your bailiff's seizing their brand new A380 at LHR. (The A380 will be flying the London-Paris route through July and August).
Here is the link to file a Small Claim online:
https://www.moneyclaim.gov.uk/web/mcol/welcome
It is easy and low cost. No lawyers required. You must produce evidence that your cases were missing for one week, reasonable costs that you incurred as a result and evidence of the damage to your cases. You have to be aware though that the purpose of luggage is to protect your belongings during travel, so they will inevitably sustain some damage. Keep your claim to what is reasonable.
Air France will respond to a summons. If you prefer not to be too litigious, you can complain to the Air Transport Users' Council. The email address is:
complaints@auc.org.uk