For an affordable Educational School Tour what is the best time to visit Paris

When to go? Paris can be visited during the whole year. If you plan to go there on a school trip, you may have other constraints, such as e.g. the school calendar. Thus, go there whenever it suits you best. I remember when I was young, people in my school went to paris in Spring (March-April) on educational trips.

How to go? This heavily depends on where you are from! If you have a critical mass of participants, I would consider to hire a coach. Note that you can use the coach to explore Paris. Train can be quite expensive. In case you want to consider this, also have a look at airfares. Another budget option would be to travel on a regular bus (Eurolines, Idbus, ...). In case you plan to travel by train or regular bus, you have to foresee a budget for local travel in Paris.

Where to sleep? You can look for an hotel outside the "boulevard périphérique". They are a cheaper than those intra muros. Quite a few of these are located close to Metro or RER stations. If you consider traveling by coach you will easily find parking facilities nearby. You can look e.g. for Ibis, F1 or Etap Hotels. They are decent and have a good price/quality ratio. But don't expect any "charm". They are functional. This discussion might also be of interest to you.

P.S. Please note that I am not affiliated with any of the following companies: Idbus, SNCF, Eurolines, Accor Hotels.