It depends on the issue, but in general I find DL can handle most AF issues. Even if they can't handle on their own, they'll put you on hold and contact AF directly for the very few items they can't do.

As for insurance, it depends on the policy. However most require the flight to be canceled and either 1)no other option given to get you to destination, or 2)alternative transportation arranged but gets you in X hours after scheduled arrival. Also, remember there may be a deductible.

Finally since this was a separate ticket did you buy insurance for it? Any insurance you bought for your other ticket won't cover the AF ticket issues, you'll have needed to bought the insurance with the AF ticket to get coverage.

All else fails, if the flight is canceled, you're entitled to a full cash refund of the ticket even if it's a non-refundable ticket. Also EU compensation rules will kick in, though I'm not sure if a strike is considered grounds to not have to pay out. No matter the EU compensation though, the cancellation means a refund, even if you flew a portion of the ticket already.