Originally Posted by jerry a. laska

It is not unusual for the short haul flight to be the problem when trying to book BA with AA miles. For example, there are any number of reports of people having difficulty finding the short haul EU segment to go with a long haul to or from NA.

You can check britishairways.com for the short haul availability but oftentimes BA does not seem to open up this availability until later. If you have avios you could always book the LHR-PAR flights using avios (4500 avios) separately.