Thanks for pointing me in the right direction. This is the solution for my problem:
SQLPLUS> connect sys/manager as sysdba;
SQLPLUS> shutdown immediate;
SQLPLUS> startup mount;
SQLPLUS> alter system enable restricted session;
SQLPLUS> alter system set job_queue_processes=0;
SQLPLUS> alter system set aq_tm_processes=0;
SQLPLUS> alter database open;
SQLPLUS> alter database DBNAME character set WE8ISO8859P1;
SQLPLUS> alter database DBNAME national character set WE8ISO8859P1;
SQLPLUS> shutdown immediate;
SQLPLUS> startup;
where DBNAME is the name of the Database of course!
On the client there needs to be a registry key:
Folder:
\HKEY_LOCAL_MACHINE\SOFTWARE\ORACLE
Key:
NLS_LANG
Value:
DUTCH_THE NETHERLANDS.WE8ISO8859P1