How can I know if an SQLexception was thrown because of foreign key violation?

Assume you're using SQL Server.

Using teh web archive - https://web.archive.org/web/20190120182351/https://blogs.msdn.microsoft.com/tomholl/2007/08/01/mapping-sql-server-errors-to-net-exceptions-the-fun-way/

try
{
    # SQL Stuff
}
catch (SqlException ex)
{
    if (ex.Errors.Count > 0) // Assume the interesting stuff is in the first error
    {
        switch (ex.Errors[0].Number)
        {
            case 547: // Foreign Key violation
                throw new InvalidOperationException("Some helpful description", ex);
                break;
            case 2601: // Primary key violation
                throw new DuplicateRecordException("Some other helpful description", ex);
                break;
            default:
                throw new DataAccessException(ex);
        }
    }

}

Case 547 is your man.

UPDATE The above is sample code and should not be used. Please follow the link as to explain why.