Answer:
Based on the given text, it can be inferred that Ms. Broussard and Ms. Mitchell have an out-group relationship. Ms. Broussard, who is presumably from a long-standing New Orleans family, sees herself as part of an in-group that Ms. Mitchell, who is not from New Orleans, does not belong to. Ms. Broussard's comment about being in New Orleans since it was part of France suggests that she sees herself as having a deeper connection to the city than Ms. Mitchell. This creates a sense of exclusion and distance between the two women.
In terms of primary vs. secondary group, it is not clear from the given text whether Ms. Broussard and Ms. Mitchell have any kind of ongoing relationship beyond this cocktail party. However, based on the context, it is likely that they are part of a secondary group, meaning that their relationship is not based on close personal ties, but rather on shared interests or circumstances (such as attending the same cocktail party).