cell number format

All phone numbers in France are 10-digits, including an initial zero. Mobile numbers start 06 or 07.
For example: 06 xx xx xx xx
or: 07 xx xx xx xx
If calling from within France dial the complete 10 digits.

If calling from outside France, drop initial '0', and the add International call prefix for the country you are dialling from and the country code for France (33).
For example: [International call prefix] 33 6 xx xx xx xx

I see you are from the USA, the International call prefix from the USA is 011, so you would dial (for example): 011 33 6 xx xx xx xx

Curious, why would the number to reserve Eiffel tower tickets be a mobile number, I would expect it to be a landline?

There is an article in Wikipedia about telephone numbers in each country, explaining this. The one for France is: https://en.wikipedia.org/wiki/Telephone_numbers_in_France

I'm on Eiffel
Tower web site and they use my cell number as account record. They require my cell number
and I am not sure of the format of the number they require. Should it include the 1 for long
distance, country code and then phone number?
Thanks

The normal way to quote a telephone number is:
+ [country code] [area code] number
The '+' means whatever International call prefix applies from wherever you are calling. Dialling '+' actually works from European mobile phones and numbers are saved on my phone that way.

The country code for the USA is 1
So the your phone's number, in standard international format, is: + 1 aaa xxx yyyy
That should work.

Thank You
Paul

without any spaces or punctuation