Open Jaw Flights

I saw $643 on Delta in March 2020 for Dallas to Paris and then return from Amsterdam to Dallas; that would be price I would snag

I use Matrix ITA website for flight planning. You can't buy from them but it is the program that travel agents used for years to recommend flights. There are a number of filters you can add, including airports of close proximity. It also covers more airlines than something like Expedia, so more options. On this site, open jaw is called 'multi-city'.
If you have a little leeway, you can also search by the best pricing in March for the number of days you can fly, or look at pricing a day or two before and after your entered dates.
You then buy on the airline's website. If you buy through a third party, then if things go wrong or need changing, you have to deal with them rather than the airline, and they aren't always the best at customer service after you have paid.
If you think you have a little time, after narrowing down a flight of interest, you could sign up for the airline promotion emails and wait a bit for some deals. Not sure if March is being covered yet, but should be soon.

I don’t know a good price - I’m not familiar with Dallas’s airfare. In general, under $1000/per economy ticket is my guideline from Chicago but it varies. I’ve seen and gotten $500 - $600 but not all destinations or times of year. Friends who live in smaller markets are often looking at $1300+ or drive to bigger cities. Others who live near Toronto or NY routinely get inexpensive fares ($500 or less). My frame of reference is all northern Midwest and east coast, though so not much help!

Google flights or kayak.com will show you the options. I find it best to book with the airline, better help if something goes wrong and easier access to seat selection, special meals for allergies and general service.

Be sure to use multi city. Booking 2 one ways is often very expensive while booking one ticket into one city and out of another is affordable. In some cities it’s cheaper than round trip, in others it’s just a little more, easily offset by time and transit savings.

We use Matrix ITA as well, for planning purposes. It's great because you can also filter by flight duration, departure time windows, etc. Seeing all the fares compared by # of stops is also helpful, as sometimes as cheaper flight that involves an extra stop may just not be worth it. If your plans are flexible, you can also play around with starting your trip in Amsterdam and returning from Paris, to see if that affects the price. Another option is to check the same itinerary (which you can do with Matrix at a glance) for partner airlines. For example, I know that Delta and Alitalia often share aircraft and routes, but the same itinerary may be slightly less on one site over the other.
Happy planning!

Matrix is good and so is Kayak.

I usually find the flights that I want then go directly to the airline. I usually go with Skyteam (Delta) since we fly with them 95% of the time. Usually the three major US airlines are close together in prices.

Open Jaw occasionally doesn't work as well as RT, in fact sometimes I have found the best prices by doing two one-way tickets. Try all options as well as click on "flexible." Sometimes you can same by flying in a day or two earlier or leaving a day or two later.

Amazing advice! Thank you all so much!

On an airline’s own site, you may need to temporarily use one-way or round-trip to see a chart of prices for every day in one month all at once. Note the cheaper days and work with them for open jaw. It may help to switch to another computer with a different IP address if possible for the final purchse. I believe many airlines watch what you are doing and adjust prices accordingly, like Amazon can.

Can’t speak to fares from Dallas. But I’d highly recommend Google Flights. You’ll find a useful tutorial here. But it’s very intuitive and easy to use.

https://scottscheapflights.com/guides/how-to-use-google-flights

We just bought multi-city SFO-AMS and CDG-SFO on the return for this fall. When there are partner/codeshare airlines combining on a route, Google Flights will present you the option to book on any of the airlines sites. In our case, we fly KLM from SFO to AMS, and Air France from CDG to SFO. Booked on Delta, but could have booked on KLM or Air France as well.

Of course too early to get a good idea of March fares, but it’d be good to play around on Google Flights and get used to it. One feature I love is the ability to track a particular flight. Say you do a search and see an interesting result for specific dates and departure times. You can click to track that itinerary, and Google Flights will send an automated email whenever the price goes up or down.

Good luck!

The only way to know a good price is to get a baseline price by checking today, a week from today for the next few months. You will know a deal when you see it. Keep a list on paper or a spreadsheet. Keep in mind the following:

Direct flight's v layovers- how much are you willing to pay for a direct flight.
Layovers- should be at least 2 hours between flights for me, between getting off the plane, possible late take off etc
Departure time- do you want the cheaper red eye or a flight that leaves at 4, lets you sleep on the plane etc. We fly LAX and a 9am flight means we stay overnight in LA which means we pay for a hotel and parking for the car, is that worth it? Does it add to the cost of the ticket, can we do the 4PM flight and save that hotel cost?
Departure from Europe- think about how early you really want to have to get up to get to the airport. For me I milk that last day and book a 6pm flight

I was recently watching a flight to Hawaii, started at $697.00 PP, direct flight, airline I wanted, times I wanted. I watched for 6 months before our trip, then when it dropped to $498 a person (3 months before our trip date) I pulled the trigger knowing I got an awesome deal. It went down before ($606., $590, $547) that but never that low.

Kayak is a great website to use because you can take a look at an airfare matrix that lists the lowest fares to and from a location on a calendar grid and see the best fares and which days to fly to get them. Another one of my strategies is to look on multiple airlines' websites for one-way fares. This often results in 30-40% savings. I do this a lot and get pretty good deals! My son is flying LAX - Istanbul - Rome - Paris - LAX in Aug / Sept and total cost was $854 by doing this. 3 different airlines. Cheapest I could find on Kayak was $1300. Another strategy is to find cheaper flights from another hub in the US and fly to that hub on a cheap flight from Dallas, and then fly to Paris. I fly to Europe from the west coast of the US and don't like to pay more than about $600 - 700 RT to and from Europe. I usually pay far less than that - in March you should have no trouble finding similar or lower prices.