Urgent guidance on Visa type and Consulate/emabassy to apply to for travelling from USA to Malta type C short stay schengen visa

I am an Indian passport holder with a valid H1B visa. Planning to attend and present at the conference in Malta from 11–15 March 2026,

While this conference is the primary purpose of my travel, I am also planning to visit France with my colleagues for five days after the conference for leisure.

Could you please advise whether I can combine both purposes (business and tourism) into a single visa application, and which visa type(tourist or business) and which consulate I should apply to?

My itinerary is as follows:
Business:

• 9 March, 2026: Flight Cincinnati (USA) → Paris (connecting flight) → Malta
• 10 March, 2026: Arrive in Malta
• 11–14 March, 2026: Attend conference

Leisure:

• 15–22 March,2026: Fly from Malta to France 

• Purpose: 

• Tourism in Toulouse, Marseille, and Montpellier; staying with a French host, my former colleague and friend, who has sent the invitation.

Additionally, is there any possibility to request an expedited appointment or faster processing so that I can obtain the visa before 10 March?