need hotel and sight suggestions for Portofino and Paris

Sorry can’t help with Portofino - a place I would love to visit myself! Paris though: the Louvre Museum is amazing, but I love the Musée d'Orsay, which houses the largest collection of Impressionist art in the world within a fabulous former railway station building. For a day trip from Paris I would recommend Giverny, Monet’s former home, or Château de Vaux-le-Vicomte. Either are totally doable from Paris using public transport, no need to pay for an expensive tour. An unusual place to visit in the city is the Père Lachaise Cemetery, a garden cemetery and the resting place of an amazing array of famous people. It’s also the site of the Mur des fédérés (Communards Wall) where the Paris commune was finally brought to a tragic end. There is a massive amount to see in Paris, best to just get a guide book and tick off some of the main sights :) Leave time to just walk the streets and absorb the atmosphere, the Marais District is a great place to do this, and would also be a lovely part of the city to stay. Place de Vosges is in the Marais, and considered to be the most beautiful historic square in Paris. Eating out: I would recommend Le Bouillon Chartier as not to be missed. Not possible to book a table and you will probably queue to get in, but it will be worth the effort.
How do you plan to get from Lucca to Paris? Consider train travel, civilised and relaxing compared to driving! You would need to take a local train to Florence, then onward to Milan. You could possibly have a night in Milan if you have time, (great shopping, fabulous cathedral, and the incomparable La Scala opera house) then take a high speed train from there to Paris, there are three each day. Check out this page on seat61.com for advice on this train trip.
https://www.seat61.com/Paris-to-Milan-by-TGV-train.htm

You might want to take the train from Milan to either Santa Margherita Ligure or Rapallo, and then take a ferry, bus or taxi to Portofino.  It takes about 15 minutes from Santa Margherita and 30 minutes from Rapallo to Portofino by ferry.  The ferry will also take you to San Fruttuoso and on to Camogli.  The train from Camogli to Santa Margherita only takes about 15 minutes.  The train from Santa Margherita to Cinque Terre takes about 50 minutes.  You could then rent a car in Santa Margherita or Rapallo and drive to Lucca.  From Lucca, take a look at Pisa, Florence, Siena, San Gimignano and Volterra.