Schengen visa(s) for two events close in time

Question

I am a Russian citizen living in Canada and there are two scientific events in Europe in which I would like to participate this June: one in Greece, one in France. There are about 10 days in-between them. I would also like to stay as a tourist in-between these events but this is optional.

Should I apply for two separate Schengen visas? If I apply for two visas, will both embassies need to take my passport at the same time? In which application should I mention tourism?

Or is it possible to apply for only one visa and provide supporting documents for both events? Which country should apply to in this case?

Answer 1

For multiple trips, within a period of two months, the country with the longest length of stay should be taken as the main destination (Article 5(1)(b) Visa Code):

if the visit includes more than one destination, or if several separate visits are to be carried out within a period of two months, the Member State whose territory constitutes the main destination of the visit(s) in terms of the length of stay, counted in days, or the purpose of stay; or

If one event is longer than the other, then that is the one you should select.

If they are both the same, then the country where your will first enter the Schengen Area (Article 5(1)(c) Visa Code):

if no main destination can be determined, the Member State whose external border the applicant intends to cross in order to enter the territory of the Member States.

The length of stay is based on what is known at the time of application (i.e. any later changes doesn't matter).

Note: The Visa Code quotes are based on the 2020-02-02 text.

Answer 2

If you stay in the Schengen area in between the events you can apply for just one visa for the length of time from before the first to after the second event. It is likely that you will be asked to proof you have enough money and make an itinerary for those 10 days.

You should apply your visa from the country which is the main reason for your stay in the Schengen area, which will be either Greece or France. If there is one of them more important (or will seem more important) that is the one which is your main reason. Otherwise you can pick the one that fits you best.

Edit:
See the answer by Mark Johnson for when not staying between the events.
When not staying you can try to apply to the country of the most important event and ask for a two entry visa and use the information for both. If that is not given you will need to apply for the other one afterwards, with the risk that you do not get that visa in time. That is the reason I write the more important rather than the first.