Transportation from CDG to Rue Cler Hotel in May?

What is your specific definition of "fairly reasonable' including money you can spend?

What time of day?

Is it acceptable for you to be sitting in bumper-to-bumper traffic or do you not mind because of luggage?

I don't know what "fairly reasonable" means in your part of the world, but the RATP Bus No. 350 from CDG will take you to the Gare de l'est for about $5, and a taxi from there to rue Cler will cost under $25. I would just take a taxi (no Uber at CDG) and hang the expense. Max. rate 55 euro for 4 people in a cab.

It depends on what you think is reasonable, how much luggage you have, how travel savvy you are, how old you are, and how many people in your group. It also depends on how far your hotel is from a metro stop. I have only taken the train (RER) back and forth from CDG. It is about 11 or so euro. But if you have two or more people, you are obviously getting close to the cost of a taxi. What I don't know is how long a taxi ride typically is, given the taxis are confined to highways/city streets. My recollection is that via RER, the ride was 30 minutes. I think to Rue Cler you'd transfer to metro at Notre Dame-St Michel.

Or just take the RER+métro to the nearest métro station (École Militaire). Depending on the time of day, probably quicker than going by road, and costing €10.30 per person.
In European cities, taxis (traditional or Uber) are not the cheapest and usually not the fastest method of transport.

Yes, there is Uber in Paris. It is as reliable there as it is elsewhere. I would not take it from CDG just because I would not want to have to deal with finding my car and driver. They are not allowed to wait at the regular taxi stands. I would take a taxi for 55€ for up to four people but without knowing your definition of reasonable, it is hard to make a specific suggestion. Reasonable is not just about cost, though that is very important, and the amount of time the trip will take but also your willingness to make transfers because you cannot get to Rue Cler to CDG without making a transfer unless you take a taxi. For example, you could take Bus 350 and then transfer to bus 42 and end up at Rue Cler having about 6€ to get there but it would take you about 2 hours to make the trip. Back when I was younger and on a very tight budget, that would have been much more reasonable to me than spending 55€ for a taxi. Nowadays, it's taxi all the way for me.

The RS Guide recommends (or at least used to recommend) the Air France bus to Opera Garnier and then the metro to Rue Cler. It does require lugging your bags, but it wasn't awful.

Well, I sure hope the RS Guide Book does not suggest taking the Air France Bus (now known as Le Bus DIrect) from CDG to Opera Garnier because their buses do not go there. The bus to take would be the Roissy Bus, which is not the same thing.

You're jet-lagged and tired when you get to CDG. In my book, it's time to treat yourself to a taxi instead of putting yourself and your travel companion(s) through more hoisting of your luggage on and off vehicles. You're spending $x,000 on the vacation and the difference between taxi fare and the cost of other transportation is worth it. Treat yourself.

I always arrive with a plan “a” and a plan “b”. Plan a is public transport researched and thought through. Plan b is a taxi, if for any reason I feel tired.

Last summer I thought I would take a taxi into Paris but I I wanted to buy my navigo pass at the airport first. I found myself looking directly at the RER station after buying my pass.. Why not? I took the RER in and transferred to the metro and walked the two blocks to my hotel. It couldn’t have been easier.

If I had been feeling tired or that I had too much luggage to handle, I would not have hesitated to take a taxi.

For a number of years I’ve been taking Le Bus Direct from CDG to the Étoile stop, and walking 20 feet to the Bus 92 stop on Ave MacMahon (direction Gare Montparnasse).

Bus 92 has numerous stops along Avenue Bosquet, which is 1 block west of rue Cler. Without knowing how many people and exactly where in the rue Cler area, it’s difficult to say if this would be the cheapest.

We took the metro to the Ecole Militaire metro stop. Our hotel was 2 blocks from it.

If you are "young" and traveling light, you can take the Metro but be aware that there are lots of stairs within the Metro and changing at stations to get to Rue Cler. Paris now has a flat taxi rate from CDG airport to the Left Bank and Right Bank of the city and the rate to Rue Cler that will drop you right at the front door of your hotel is E55. The trip took me past the Arc de Triomphe at the top of the Champs Elysees and over the bridge near the Eiffel Tower so you got to see some of the major sights enroute to your hotel. So very easy.

Just to clarify, if you do opt for public transportation, you first need to take the RER from the airport (local train) then depending on hotel location you will either get off or transfer to the metro. That taxi ride sounds wonderful!

After a 20-24 hr travel day .. I get in a taxi.. its 55 euros to left bank.. done and done , door to door.

Thank you for all your wonderful responses - it's great to see that there other other options than just taxis or Uber. I guess I'll play it by ear and see how tired I feel after my flight over there.