If your travel company is comfortable with cycling, Velib is the least stressful form of transportation in Paris. You pay a daily fee, which is very low, and then you can take a velib bicycle to cycle around. The first 30 minutes of each trip are always free of charge. This actually means that you can ride for free as long as you change bicycles every 30 minutes.
It is my favorite form of transportation in Paris, since it gives the shortest travel times from almost any point to any other point in Paris. Using conventional public transport typically takes you much longer, given the transits you often have to make. BTW transit often involves stairs and medium to long walks.
If you are not comfortable with cycling, I would try to use as many buses as possible and try to plan ahead. For example, don't go to Notre Dame right after the Eiffel tower. You will lose some time in the metro.
Personally I've never bought a day ticket in Paris. You can buy single tickets in groups of 10 at almost if not all metro stations. The vending machines do accept all major credit cards. I often buy 10 tickets. One ticket is valid for one trip. On a busy day I would use 4 tickets max. So, if you don't intend to spend much time in the metro, a day ticket is overkill. When buying the groups of tickets, try to avoid the big train stations (Gare du Nord, Montparnasse) since they often have long waiting queues for the vending machines. If you are uncomfortable with the vending machine, ask the staff at the so called "guichets". You can buy them there as well with all major credit cards.
I have lived in Paris, so whenever I am in Paris these days I tend to ignore the traditional parts, but I would really recommend going to the Sacré-Cœur. Be aware that the Sacré-Cœur is on top of a hill and it involves quite some climbing up the stairs. But the sight is worth it! I think you can get to the top by bus, but I am not sure.
Also the parks, especially with nice weather, are worth a visit. I would recommend Jardins du Luxembourg and Tuileries gardens.
If you are in Paris at the weekend, consider going to the many "Brocantes", "Puces" or flea markets. The best advice is to be there early to experience these flea markets to the fullest. The one I used to visit frequently is :
Puces de la Porte de Vanves (French) This was because I used to live around the corner. There are many. I think that there is even a newspaper sold at any kiosk telling you all the flea markets in Paris.
Another nice touristic point to visit is the Pantheon with its Foucault pendulum. This is nice to combine with both the Jardins du Luxembourg, the Notre Dame and Latin Quarter.
If it is your first time in Paris and you want to get a small taste or first impression of what to expect, I suggest watching some movies set in Paris. I would recommend: Amelie and Midnight in Paris. The latter is about a guy traveling with his in-laws to Paris (be aware) ;)