If you are coming from Amsterdam, Lille is by far the best entry point. From there you have high speed trains to plenty of destinations: Lyon, the Mediterranean coast, Bordeaux, Toulouse, Rennes, Strasbourg, ... The trains actually bypass Paris. However, it makes no sense to try to avoid Paris at any cost. It can make sense to travel through Paris. There are more frequent and better connections, and it can be cheaper. This options should therefore always be checked.
It is also interesting to note that Lille can easily be reached from Amsterdam by classical IC trains via Brussels or Antwerp. This option takes much longer though.
Passing through Luxembourg does not really make sense, even if your destination is Strasbourg. It is much easier to travel through Lille. From there you have direct trains to Strasbourg. Or you can travel through Paris. You will arrive at the Paris North station ("Gare du Nord"). The trains to Strasbourg leave from the Paris East station ("Gare de l'Est"). These stations are next to each other. It's a little 10 minute walk from one station to another. Through Lille, it takes +- 6h30 to Strasbourg. Through Luxembourg it is much much longer and you have to change in Brussels, and perhaps Luxembourg and Metz, as direct trains from Brussels to Strasbourg are very scarce (2 per day). In any case, count at least 8 to 9 hours if you travel that way from Amsterdam to Strasbourg. These are classical trains, and the road from Brussels to Luxembourg is quite scenic. If you prefer that ... Otherwise, if your destination is Metz, passing through Luxembourg can make sense.
There are two other options. The daily German ICE train from Amsterdam to Basel calls at Offenburg, just opposite Strasbourg, on the other side of the Rhine. This is probably the quickest option. The City Night Line train from Amsterdam to Zurich also calls at Offenburg, early in the morning. From Offenburg you can proceed by a local train. That's straightforward.