Here's the "do something on each db" template I use, slightly adapted to your example:
--Create a table to hold the query results
CREATE TABLE #licenselist
(dbid smallint, dbname sysname, system_license varchar(99));
DECLARE @fixedname nvarchar(150);
--Include or exclude whatever databases you want
DECLARE dbCursor CURSOR FOR
SELECT REPLACE(QUOTENAME(name),'''','''''') --For db names with annoying characters
FROM master.sys.databases
WHERE state_desc = 'ONLINE'
AND HAS_DBACCESS(name) = 1 --Added at @SolomonRutzky's suggestion
AND name NOT IN ('master','msdb','model','tempdb');
OPEN dbCursor;
FETCH NEXT FROM dbCursor INTO @fixedname;
WHILE @@FETCH_STATUS = 0
BEGIN
EXEC ('USE ' + @fixedname + ';' +
'INSERT INTO #licenselist
SELECT DB_ID() as dbid, DB_NAME() as dbname, ParamValue as system_license
FROM Table1
WHERE paramname = ''SYSTEM_LICENSE'';');
FETCH NEXT FROM dbCursor INTO @fixedname;
END;
CLOSE dbCursor;
DEALLOCATE dbCursor;
SELECT * FROM #licenselist
DROP TABLE #licenselist
EDIT: streamlined a bit, removed the raw @dbname variable and instead fixed it in the original query.