Is Rail Pass the right choice for my Itinerary..

Others are more familiar with the French, Swiss, and all Italian legs than I, but right now, with advance purchase on the Bahn website, for a group of 7 adults (all over 14) in 2nd class, you could get tickets for the EC that leaves Venice at 13:34 and gets to Munich at 20:25, with reservations, for €310. The EC at that time is a direct train. If you wanted to leave earlier, you could get Verona to Munich for €235 with reservations, but you'd have to book Venice to Verona separately. That leaves you with about $3100 for the other four days of travel. I'll let others advise you as to the other legs, but it doesn't look like the rail pass would pay.

When are you going, how long will you be in Switzerland, and how old are the kids? With journeys like that, which are best served by the high-speed TGV (in France) and ES trains (in Italy), you can generally do much better with advance-purchase discount tickets (as low as 9 euros per person in Italy, which is less than the reservatin fee for the ES trains). A Swiss pass or Half-Fare card may be useful in Switzerland if you are staying more than a few days. Children under 16 are free with either of those passes.

Lee, Lola
Thanks for your response. I have been researching on each of the train segments and I believe in general, it is possible to get a second-class fare that is much cheaper compared to the EuRail pass. Is there any benefit to travelling first-class apart from the comfort? Is it easier to get reservation in first-class?

If you have passes, you will also have to buy seat reservations for either Spiez or Brig to Milan. What are your travel dates?

You almost certainly can do better buying the tickets yourself. If you pre-purchase, the deals can be significant. Plus it sounds like you'll need a 5 country pass, just to travel quickly through Austria and a small portion of Germany. Plus the adults must buy 1st class passes, yet you'll need to sit in 2nd class with the kids (who can get the 2nd class passes). So you waste money that way. For the trains you are taking, 2nd class is more than adequate.

The Paris-Interlaken segment is not available for online purchase at the BAHN website. On RailEurope the cost for an Economy ticket is $225 on TGV
Is there any pass other than EuRail that can give me discounted price on this trip? We definitely want to travel in a high-speed train.

Forgot to mention that we will be travelling in July and stay in Interlaken for 2 days.

Highly unlikely a pass would be worth in your case! trains listed on 3 and 4 also require reservations

You said you will be traveling in July, but you didn't list the dates for each train trip. The best fares for point-to-point tickets will depend upon how many discount fare tickets, if any, are available for those dates. The cheapest fares for Paris-Interlaken are already gone for July. However, I entered some arbitrary July dates on the SNCF site and found a fare as low as €93.40. Interlaken to Florence: 1. Interlaken Ost-Milan (one connection in Spiez). Booked now on the Swiss Rail site, you can get a discount fare as low as 33.00 CHF.
2. Milan-Florence: Booked now on the Trenitalia site, you can get a Mini fare as low as €9.00. Florence to Rome: Booked now on the Trenitalia site, you can get a Mini fare as low as €9.00. Rome to Venice: Booked now on the Trenitalia site, you can get a Mini fare as low as €9.00. Venice to Munich: Booked now on the German Rail site, you can get a discount fare as low as €49.00. There is one direct daytime train. For other daytime departure times you will need to connect in Verona. There also is a direct CNL night train for which you can get discount fares by booking now on the German Rail site.