Unfortunately technical problems do sometimes happen at airports.
CDG has been relatively free of massive technical problems (although some industrial actions can create big problems once in a while). But in case of serious technical problems (often software), bags could be delayed for a while. LHR has been subject to two massive problems in the past year that created chaos, and I was subject to one them.
Perishable goods is a risk that you are taking and they are not covered by any kind of insurance, at least not by the airline. The airline would usually reimburse you for the purchase of essentials (clothes, toiletry and medicine) that you need while your bags are delayed. Each airline has a different policy and factors such as class of travel, elite status and the length of delays play a role. AF is usually good but do not expect that you will be able to buy expensive clothing and the like. I think that DL has a policy of $50 per day of delay. BA reimbursed me for the necessary purchase of a cheap suit, shirt, tie and toiletries as this was a business trip with a five-day delay. But I was in business class and BAEC Gold (OW Emerald). In any case, the Montreal convention states that the maximum liability is around $1,500. The DOT has a higher maximum, but not sure that this applies in your case. However, this is the overall maximum liability of the airline in case of full loss, but purchase of essentials can be part of that maximum. Of course, you would need the receipts.
If you were going back home, as seems to be your case (few details given), the airline would usually not cover any purchase of essentials.
No other compensation is to be expected.
How long the delay is going to be is impossible to predict.