Refer to operating carriers' allowances, not marketing carrier (unless FB publishes a rule that its allowance is the marketing carrier's in case of a codeshare). So you have an FB allowance and an IB allowance.

Where those allowances differ, the bag allowance of the Most Significant Carrier for your route applies. As the IB flight crosses from Europe-America, while the FB flight is intra-Europe, then the IB allowance should apply.

Of course this assumes that the check-in staff follow the rule, which I am not convinced they would.

I have had BA tickets with BE-BA connections, and the BE allowance was only one bag, but should - according to this rule - have been the full BA allowance.