Does a composite primary key break the first normal form?
No, this is quite normal (pun intended). The criteria is

First Normal Form:
Tables are said to be in first normal form when:

The table has a primary key.
No single attribute (column) has multiple values.
The non-key attributes (columns) depend on the primary key.


None of these requirements for 1NF is violated by the design you propose.
For instance a Junction Table created to normalize a many-to-many relationship will always have a composite Primary Key, with each component being also a Foreign Key into one of the joined tables.